Spatial ordering of charge and spin in quasi one-dimensional Wigner molecules
柴油机喷雾混合的场效应分析方法研究_刘福水
第27卷(2009)第4期内 燃 机 学 报Tran s acti on s of CS I CEVol.27(2009)No.4 文章编号:100020909(2009)0420339205272053 柴油机喷雾混合的场效应分析方法研究刘福水,白 冰,李向荣(北京理工大学机械与车辆学院,北京100081)摘要:柴油机燃烧系统的设计及匹配一直是柴油机研究的重点。
提出了一种新的柴油机燃烧系统场效应分析方法,针对喷雾混合过程进行微观及宏观仿真分析研究。
场效应分析方法从燃油浓度场和速度场对混合过程的影响规律入手,将这两个场量对传质的作用通过场效应角进行量化,从而对燃烧系统的优劣进行定量的评价,指导燃烧系统的设计或优化匹配。
以喷雾锥角的匹配为例应用场效应分析方法进行了仿真研究,并在单缸机上进行了试验验证,证明了场效应分析方法的有效性和实用性。
关键词:柴油机;燃烧系统;场效应;喷雾;仿真中图分类号:TK412.2 文献标志码:AResearch on F i eld Effecti on Ana lyz i n g M ethod of D i esel Spray and M i x i n g ProcessL IU Fu2shu i,BA I B i n g,L I X i a ng2rong(School of Mechanical and Vehicle Engineering,Beijing I nstitute of Technol ogy,Beijing100081,China)Abstract:Matching of diesel combustion system is the core of diesel engine research.A new analyzingtool named field effection analyzing method is p r oposed in this paper t o si mulate the Sp ray,the m ixturefor mati on and the co mbusti on p r ocess in the chamber of diesel engine in both m icro and macr o as pect.T womain factors of this method are fuel concentration and velocity of flow field.The action of t wo fact ors onmass transfer is quantified by the Field Effecti on Angle,and t o evaluate the combustion system.The matc2hing of s p ray angle as an examp le to conduct the si mulati on by using field effection analyzing method.Ver2ification was made in a single cylinder engine,and the study shows that the field effecti on analyzing meth2od is an effective and app licable method.Keywords:D iesel engine;Combusti on system;Field effecti on;Sp ray;CFD si mulation引言 如何实现柴油机的高效快速燃烧一直是柴油机研究工作者努力的目标。
半导体一些术语的中英文对照
半导体一些术语的中英文对照离子注入机ion implanterLSS理论Lindhand Scharff and Schiott theory 又称“林汉德—斯卡夫—斯高特理论”。
沟道效应channeling effect射程分布range distribution深度分布depth distribution投影射程projected range阻止距离stopping distance阻止本领stopping power标准阻止截面standard stopping cross section退火annealing激活能activation energy等温退火isothermal annealing激光退火laser annealing应力感生缺陷stress-induced defect择优取向preferred orientation制版工艺mask-making technology图形畸变pattern distortion初缩first minification精缩final minification母版master mask铬版chromium plate干版dry plate乳胶版emulsion plate透明版see-through plate高分辨率版high resolution plate，HRP超微粒干版plate for ultra—microminiaturization 掩模mask掩模对准mask alignment对准精度alignment precision光刻胶photoresist又称“光致抗蚀剂”。
负性光刻胶negative photoresist正性光刻胶positive photoresist无机光刻胶inorganic resist多层光刻胶multilevel resist电子束光刻胶electron beam resistX射线光刻胶X—ray resist刷洗scrubbing甩胶spinning涂胶photoresist coating后烘postbaking光刻photolithographyX射线光刻X-ray lithography电子束光刻electron beam lithography离子束光刻ion beam lithography深紫外光刻deep—UV lithography光刻机mask aligner投影光刻机projection mask aligner曝光exposure接触式曝光法contact exposure method接近式曝光法proximity exposure method光学投影曝光法optical projection exposure method 电子束曝光系统electron beam exposure system分步重复系统step-and—repeat system显影development线宽linewidth去胶stripping of photoresist氧化去胶removing of photoresist by oxidation等离子［体]去胶removing of photoresist by plasma 刻蚀etching干法刻蚀dry etching反应离子刻蚀reactive ion etching，RIE各向同性刻蚀isotropic etching各向异性刻蚀anisotropic etching反应溅射刻蚀reactive sputter etching离子铣ion beam milling又称“离子磨削”。
Surface-induced ordering in thin uniaxial liquid crystal lms
Surface-induced ordering in thin uniaxial liquid crystalfilmsHyunbum Jang and Malcolm J.GrimsonDepartment of Physics,University of Auckland,Auckland,New Zealand͑Received3May1999;revised manuscript received23August1999͒The interface localization transition in thin uniaxial liquid crystalfilms with competing surfacefields has been studied using Metropolis Monte Carlo simulations.The model is constructed from a lattice of continu-ously orientable interacting spins,and the Hamiltonian contains both bilinear and biquadratic contributions. The biquadratic contribution to the Hamiltonian is familiar from the Lebwohl-Lasher model,and accounts for the particle anisotropy in a liquid crystal.The head-tail asymmetry of the molecules in a uniaxial liquid crystal is taken into account through a bilinear contribution familiar from the classical ferromagnetic Heisenberg model with exchange anisotropy⌳.The critical temperature T c,characterizing the interface localization transition within the uniaxial liquid crystalfilm,depends strongly on the relative magnitudes of the bilinear and biquadratic interactions between the spins.For systems dominated by the biquadratic interaction,T c is found to be close to the bulk critical temperature of the system.But as the biquadratic interaction strength is reduced, T c departs markedly from the bulk critical temperature of the system.PACS number͑s͒:64.70.Md,75.40.Mg,75.10.Hk,75.40.CxI.INTRODUCTIONThe interface localization transition in thin ferromagnetic films with competing surfaces has been the subject of many recent investigations.Extensive studies of the Ising ferro-magnet by Binder and co-workers͓1–4͔distinguished the nature of this transition from the bulk phase transition and the wetting transition observed in thinfilms with cooperative surfacefields.Both the Ising and Heisenberg models have been widely used to model the magnetic properties of mate-rials.In the classical Heisenberg model,the magnetic spins can rotate through all possible orientations,and this distin-guishes it from the Ising model,in which the spins are re-stricted to orientations along a particular axis,conventionally denoted as the z axis.For thin ferromagneticfilms,the phase behavior of the Heisenberg spin system has been studied under the action of competing surfacefields with different types of model anisotropy͓5,6͔.For sufficiently large values of the anisotropies,the characteristic interface localization transition of thin ferromagnetic Isingfilms with competing surfacefields is recovered.But for small anisotropies the phase behavior of the thin ferromagnetic Heisenbergfilm has a markedly different character.The role of surface effects in the physics of nematic liquid crystals is of great significance because of their application in the thin visual display cells.The presence of bounding surfaces promotes competing types of molecular alignment between surface and bulk that provide a capacity to modify the orientation of the nematic axis.Conventionally one dis-tinguishes between parallel͑or random planar or homoge-neous͒and perpendicular͑or homeotopic͒forms of surface alignment,and most theoretical studies of thin nematicfilms with surface alignment centered on the use of Landau–de Gennes theory͓7͔.Simulation studies have primarily fo-cused onfilms with free surfaces and no surfacefields͓8͔. However,Chiccoli et al.͓9͔recently performed a Monte Carlo simulation study of the topological defects in thin nematicfilms with hybrid boundary conditions.These stud-ies used a lattice spin model,the Lebwohl-Lasher model,confined between two surfaces,one of which favored a nor-mal spin alignment while the other preferred a tangential orientation of the spins.The Lebwohl-Lasher model͓10͔is a lattice spin version of the famous Maier-Saupe model of an anisotropic liquid.The molecules are represented by headless spins that can beviewed as rodlike anisotropic particles,and the coupling be-tween translational and orientational degrees of freedompresent in a real nematogen are neglected.Thus it is an ap-propriate model for orientational ordering in a solid.How-ever,it is believed that the model still reveals the essentialtransitional properties of liquid crystals near the nematic-isotropic phase transition,and it has been extensively used incomputer simulation studies of liquid crystals͓11–18͔.Athigh temperatures,the spins rotate through all possible ori-entations,and the system is an isotropic state.But at suffi-ciently low temperatures the spins display a spontaneous ori-entational ordering.The order parameter for the nematic-isotropic phase transition is the orientational order parameter ͗P2͘.This measures the degree of orientation of the molecu-lar axes along the director,which is the preferred direction oforientation.As a result of the continuous degeneracy of thenematic ordering in the absence of an externalfield,the ori-entation of the director varies during the simulation.Theorientation of the director can however be pinned by theapplication of a one-body externalfield that aligns the direc-tor parallel to thefield͓12,13͔.The molecules of a uniaxial liquid crystal possess a head-tail asymmetry in addition to their rodlike anisotropy.Asimple model to investigate the physics of uniaxial liquidcrystals,based on the Lebwohl-Lasher model,was intro-duced by Biscarini et al.͓15,16͔,in which the biquadraticinteraction of the Lebwohl-Lasher model was supplementedby a bilinear exchange interaction between the spins familiarfrom the classical Heisenberg model of ferromagnetism.Such a model wasfirst introduced to study orientationalphase transitions in molecular crystals͓19͔,and has also pre-viously been applied to magnetic systems in which the ex-change interaction between the magnetic spins possessesPHYSICAL REVIEW E JANUARY2000VOLUME61,NUMBER1PRE611063-651X/2000/61͑1͒/511͑8͒/$15.00511©2000The American Physical Society‘‘quadropolar’’as well as‘‘dipolar’’characteristics͓20͔.In the Lebwohl-Lasher model,the biquadratic interaction favors a parallel alignment of the spins in a preferable direction below a critical temperature T c N.At high temperatures the spin orientation is isotropic.In the absence of an external field the classical Heisenberg model only displays a sponta-neous nonzero magnetization at zero temperature.However, if a sufficiently large bilinear exchange anisotropy is in-cluded in the Hamiltonian for the Heisenberg model,Ising-like behavior is recovered in which the spins order sponta-neously below a critical temperature T c F even in the absence of an externalfield.This paper investigates the phase behavior of thin uniaxial liquid crystalfilms with competing surfacefields.In Sec.II a full description of the model is given and the details of the Monte Carlo simulation method are presented.The depen-dence of the equilibrium phase behavior of thefilm on the strength of the biquadratic interaction is studied in Sec.III, while the corresponding order parameter structures in the film are discussed in Sec.IV.The temperature dependence of the interface localization transition is investigated in Sec.V and the paper concludes with a summary of the keyfindings in Sec.VI.II.MODELKrieger and James͓19͔introduced a lattice spin model defined by the HamiltonianH KJϭϪ͚͗i,j͓͘J͑S i•S j͒Ϫ͑S i•S j͒2͔͑1͒to describe the successive orientational transitions in molecu-lar crystals.In the Hamiltonian͑1͒,S iϭ(S i x,S i y,S i z)is a unitvector representing the i th spin,and the notation͗i,j͘means that the sum is restricted to nearest-neighbor pairs of spins. The coupling constants J andcharacterize the magnitudes of the bilinear and biquadratic exchange interactions between the spins respectively.When Jϭ0and 0,the model re-duces to the Lebwohl-Lasher model͓10͔,and the system displays nematic order below a critical temperature T c/in which the spins spontaneously orient in a preferred direction termed the director.However,in the absence of any external field,the orientation of the director is notfixed in space due to thefluctuation in the spin orientations.Whenϭ0and J 0,the model reduces to the familiar classical Heisenberg model of magnetism,and for ferromagnetism JϾ0.When both J 0and 0,the model has been used to describe uniaxial liquid crystals in which ferroelectric and antiferro-electric ordering are both possible͓15,16͔.The molecules of a uniaxial liquid crystal are characterized by a head-tail asymmetry,and hence a short ranged bilinear interaction supplements the biquadratic spin-spin interaction of the Lebwohl-Lasher model.This paper focusses on a lattice spin model with a gener-alization of the Krieger-James Hamiltonian͑1͒that allows for anisotropy of the bilinear exchange interaction withH0ϭϪ͚͗i,j͕͘J͓͑1Ϫ⌳͒͑S i x S j xϩS i y S j y͒ϩS i z S j z͔Ϫ͑S i•S j͒2͖,͑2͒where⌳is the exchange anisotropy which determines the strength of the bilinear exchange interaction of the x and y components of the spin.Whenϭ0and⌳ϭ0,the model reduces to the familiar classical Heisenberg model of mag-netism.The system under consideration here is a three-dimensional thin uniaxial liquid crystalfilm offinite thick-ness D under the action of competing surfacefields with HamiltonianHϭH0Ϫ͚isurface1H1•S iϪ͚isurface DH D•S i,͑3͒where H1and H D are the applied surfacefields.We consider a simple cubic lattice of size LϫLϫD,in units of the lattice spacing,and apply periodic boundary condition in the x and y directions.Free boundary conditions are applied in the z direction which is offinite thickness D.The system is subject to competing surfacefields applied a layer nϭ1and nϭD of thefilm withH1ϭh zˆ␦i1,͑4͒H DϭϪh zˆ␦iD,͑5͒giving a HamiltonianHϭH0Ϫh͚ͩisurface1S i zϪ͚isurface D S i zͪ.͑6͒Afilm thickness Dϭ12and surfacefield strength hϭϪ0.55were used throughout to aid comparison with the cor-responding Ising and Heisenbergfilms investigated else-where͓1,2,5,6͔.The results do not depend significantly on the value of h,and Dϭ12corresponds to the crossover re-gime between wall and bulk dominated behavior for thin Isingfilms͓2͔.In thinnerfilms it is difficult to distinguish between‘‘interface’’and‘‘bulk’’phases in thefilm,since all layers of thefilm feel the effect of the competing surface fields rather strongly.For thickerfilms the surfaces of the film only interact close to the bulk critical point.Results are reported for lattices of size Lϭ32.A number of additional simulations were performed for Lϭ64and128, but no significant differences were found from the results presented here for non-critical values of the parameters.The Metropolis algorithm͓21͔was used in the Monte Carlo simulations with trial configurations generated from Barker-Watts͓22͔spin rotations.The magnitude of the maximum spin rotation was adjusted to ensure approximately50%of trial configurations were rejected in the bulk equilibrium state.The‘‘magnetic’’order of thefilm is characterized by z component of the magnetization for thefilm,M zϭ1D͚nϭ1DM n z,͑7͒where the z component of the magnetization for the n th layer of thefilm:M n zϭ1L2͚S i z.͑8͒512PRE61HYUNBUM JANG AND MALCOLM J.GRIMSONIn addition to the‘‘magnetic’’order M z,in studying this model,it is also necessary to consider the‘‘nematic’’order resulting from the biquadratic exchange term in the Hamil-tonian.In common with studies of the nematic-isotropic phase transition in liquid crystals,the orientational order pa-rameter for thefilm isP2ϭ1D͚nϭ1DP2n,͑9͒where the orientational order parameter for the n th layer of thefilm isP2nϭ1L2͚P2͑S i•zˆ͒,͑10͒and P2(S i•zˆ)is the second Legendre polynomial.The pres-ence of the unit vector zˆin Eq.͑10͒indicates that the director is assumed to be in a time-independent alignment along the z axis.One effect of the applied surfacefields is to suppress fluctuations in the orientation of the director,which is then fixed in the z direction perpendicular to the plane of thefilm. Equilibrium averages of the order parameters were typicallytaken over2ϫ105Monte Carlo steps per spin͑MCS/spin͒with initial transients ignored.III.INTERFACE LOCALIZATIONAND THE BIQUADRATIC EXCHANGE INTERACTION For thin ferromagnetic Isingfilms with competing surface fields,an interface localization transition is observed that is absent in the corresponding isotropic Heisenberg model.If the bilinear exchange interaction in the Heisenberg model is made anisotropic,then the interface localization transition is recovered for sufficiently strong anisotropies.Here the changes in the phase behavior of the thinfilm resulting from the introduction of a biquadratic exchange interaction are investigated.First we focus on a system with a bilinear exchange an-isotropy of⌳ϭ0.1.Forϭ0,this system corresponds to a thin ferromagnetic Heisenbergfilm with weak exchange an-isotropy whose phase behavior is like that observed for the isotropic Heisenberg system.The orientational order param-eter,͗P2͘,and the z component of the mean magnetization per spin,͗M z͘,for thefilm are shown in Fig.1as a function of the strength of the biquadratic exchange interaction for0.1ϽϽ1at reduced temperatures of T*ϭk B T/Jϭ1.0and1.5.In all cases the initial spin configuration was a ferromag-netically ordered state with S i zϭϩ1for all i.At the lower temperature of T*ϭ1.0,both͗P2͘and͗M z͘are smooth monotonic increasing functions of,and nonzero for all. This is as expected,since even atϭ0thefilm displays a well-developed ferromagnetic order in the z direction at T*ϭ1.0.The degree of order of the spins is enhanced asincreases.However,at the higher temperature T*ϭ1.5,for smallthefilm is in a paramagnetic state with no spontane-ous directional ordering of the spins and͗M z͘ϭ0.But there is a sharp increase in͗M z͘forϾ0.3,indicating the onset of ferromagnetic order.The paramagnetic-ferromagnetic phase transition in thefilm is characterized by a critical value of the biquadratic coupling constantcϭ0.32Ϯ0.01for T*ϭ1.5.However at T*ϭ1.5,in marked contrast to thedependence of͗M z͘,͗P2͘is seen to be a smoothly increasing function of with͗P2͘Ͼ0for all.Thus while the qualitative form ofthedependence of͗P2͘is the same at both temperatures, thedependence of͗M z͘is qualitatively different.Note that a temperature of T*ϭ1.5is above a critical temperature T c, characterizing the interface localization transition in a thin ferromagnetic Heisenbergfilm with an exchange anisotropy ⌳ϭ0.1͓6͔.No spontaneous magnetization of thefilm is ob-served for TϾT c.However,a small nonzero value ofis sufficient to give rise to spontaneous ferromagnetic ordering with͗M z͘Ͼ0even though TϾT c for the Heisenbergfilm in whichϭ0.Thus the addition of a biquadratic exchange interaction clearly plays an important role in controlling the order-disorder characteristics of the system.Next the dependence of the phase behavior on the bilinear exchange anisotropy⌳is investigated for0р⌳р1.Over this range of⌳,in the thinfilm geometry under investigation here with Dϭ12and hϭϪ0.55,the characteristic phase be-havior of the anisotropic Heisenberg ferromagneticfilm with ϭ0has been shown͓6͔to change from Heisenberg-like to Ising-like.Figure2shows results for thefilm order param-eters͗P2͘and͗M z͘as a function of the ferromagnetic ex-change anisotropy⌳for two cases:͑i͒T*ϭ1.0andϭ0.1 and͑ii͒T*ϭ1.5andϭ0.3.It can immediately be seen that the qualitative dependence of͗P2͘and͗M z͘on the control variable is similar to that seen in Fig.1.However,thefigure shows that͗M z͘ϭ0when the model has an isotropic ex-change interaction⌳ϭ0.In this case the bilinear component of the model Hamiltonian reduces that of a classical isotropic Heisenberg model,and ordered spin states are quickly de-stroyed atfinite temperature.Increasing the value of⌳leads to spontaneous spin alignment along the z axis and ferromag-netic order.In contrast,the orientational order parameter,͗P2͘,is a smoothly increasing function of⌳with͗P2͘Ͼ0 for all⌳.It is notable that for T*ϭ1.0,there is a sharp decrease in͗M z͘toward zero for⌳Ͻ0.1.While atthe FIG.1.The orientational order parameter͗P2͑͘open symbols͒and z component of the magnetization per spin͗M z͑͘solid sym-bols͒for different valueswith⌳ϭ0.1at temperatures of T*ϭ1.0and1.5.PRE61513SURFACE-INDUCED ORDERING IN THIN UNIAXIAL...higher temperature of T *ϭ1.5,the decrease in ͗M z ͘toward zero with decreasing ⌳occurs at much higher values of ⌳,and is spread over a much larger range of ⌳values than for T *ϭ1.0.IV.STRUCTURE WITHIN THE FILMA greater insight into the phase behavior of the film seen above is obtained from the information contained in the layer order parameters across the film.The layer orientational or-der parameter ͗P 2n ͘across the film for temperature T *ϭ1.5and biquadratic exchange anisotropy ⌳ϭ0.1is shown in Fig.3͑a ͒for a set of values of the biquadratic interaction strength in the range 0.2ϽϽ1.The corresponding results for the film orientational order parameter ͗P 2͘are contained in Fig.1.For ϭ0.2and 0.3,the profiles of ͗P 2n ͘across the film are symmetric about the center of the film,and the mini-mum value of ͗P 2n ͘is located at the center of the film.This indicates that there is an enhanced ordering of the spins near the surface due to the applied surface fields.An isotropic state is observed in the bulk of the film.However,for ϭ0.4,the location of the minimum value in ͗P 2n ͘is dis-placed from the center of the film toward the surface,and is located in the surface layer for Ͼ0.4.Moreover,in the bulk of the film the spins order spontaneously and as a conse-quence ͗P 2n ͘within the bulk increases with increasing .For Ͼ0.4,͗P 2n ͘in the surface layers is less than the bulk value.This is a result of the competition between ordering tendencies of the applied surface fields and the disorder in the surface layers introduced by the free boundary conditions on the film.For Ͼ0.4the surface field strength is insuffi-cient to suppress the enhanced fluctuations in the spin orien-tation in the surface layers where the number of nearest neighbors are smaller.Thus,for larger ,Ͼ0.4,the spin ordering within the film occurs principally within the bulk of the film.However,for Ͻ0.4,the isotropic phase is ob-served in the bulk of the film,and this produces a low valueof ͗P 2n ͘in middle of the film.Ordering of the film is then principally found at the surfaces.The qualitative difference in film behavior between the results for Ͻ0.4and Ͼ0.4can be observed immediately in the magnetization profiles across the film,͗M n z ͘,pre-sented in Fig.3͑b ͒.The figure shows the surface fields lo-cally constrain the spins to align in a negative direction near one surface and in a positive direction near the other surface.In the bulk of the film,the mean spin orientation of the layers varies smoothly from one surface to the other.For ϭ0.2and 0.3,the interface between regions of negative and posi-tive magnetization is not localized,and the point of zero magnetization is located at the center of the film.However,for ϭ0.4,the interface is shifted toward the surface and disappears into the film surface with increasing .Note that the minimum values of ͗P 2n ͘for each are located intheFIG.2.The orientational order parameter ͗P 2͑͘open symbols ͒and z component of the magnetization per spin ͗M z ͑͘solid sym-bols ͒for different values ⌳at a temperature of T *ϭ1.0with ϭ0.1and at a temperature T *ϭ1.5with ϭ0.3.FIG.3.͑a ͒The layer orientational order parameter across the film ͗P 2n ͘,and ͑b ͒the layer magnetization across the film ͗M n z ͘for different values of with ⌳ϭ0.1at a temperature T *ϭ1.5.All results were obtained from an initial spin state of S i z ϭϩ1for all i ,competing surface fields with h ϭϪ0.55and a film thickness of D ϭ12.514PRE 61HYUNBUM JANG AND MALCOLM J.GRIMSONsame layer as the point of zero magnetization in the ͗M n z ͘profiles.For smaller the spins in the center of the film are in an isotropic state,and the interface between regions of negative and positive magnetization is not localized.How-ever,for larger nematic ordering occurs in the bulk of the film and promotes ferromagnetic order there,leading to a localization of the interface between regions of negative and positive magnetization at or near the surface of the film.The bilinear exchange anisotropy ⌳can play a similar role in controlling the existence and location of an interface localization transition in the film.The layer orientational or-der parameter profile ͗P 2n ͘and layer magnetization profile ͗M n z ͘across the film at a temperature T *ϭ1.5with ϭ0.3is shown in Fig.4for different values of ⌳in the range 0.1Ͻ⌳Ͻ1.For ⌳ϭ0.1neither nematic nor ferromagnetic order is observed in the system.Both the minimum value of ͗P 2n ͘and the interface between regions of negative and positive magnetization are located at the center of the film.However for ⌳Ͼ0.1,the interface between regions of negative and positive magnetization becomes localized,and is shifted to-ward the surface together with the minimum in ͗P 2n ͘.V.TEMPERATURE DEPENDENCEThe temperature dependence of the order parameter pro-files ͗P 2n ͘and ͗M n z ͘across the film is shown in Fig.5for a biquadratic coupling constant ϭ0.2and a bilinear exchange anisotropy ⌳ϭ0.1.At high temperatures T *ϭ1.4and 1.6,an isotropic paramagnetic phase is observed in the film,and the system shows no spontaneous orientational ordering.The minimum value of ͗P 2n ͘and the interface between regions of negative and positive magnetization are both located attheFIG.4.͑a ͒The layer orientational order parameter across the film ͗P 2n ͘,and ͑b ͒the layer magnetization across the film ͗M n z ͘for different values of ⌳with ϭ0.3at a temperature T *ϭ1.5.All results were obtained from an initial spin state of S i z ϭϩ1for all i ,competing surface fields with h ϭϪ0.55and a film thickness of D ϭ12.FIG.5.͑a ͒The layer orientational order parameter across the film ͗P 2n ͘,and ͑b ͒the layer magnetization profiles across the film ͗M n z ͘for different temperatures with ϭ0.2and ⌳ϭ0.1.All results were obtained from an initial spin state of S i z ϭϩ1for all i ,com-peting surface fields with h ϭϪ0.55and a film thickness of D ϭ12.PRE 61515SURFACE-INDUCED ORDERING IN THIN UNIAXIAL ...center of thefilm.However,as the temperature is reducedfrom T*ϭ1.3to1.0,the interface between regions of nega-tive and positive magnetization becomes increasingly local-ized and is shifted toward the surface,disappearing into the surface at low temperatures.This interface motion across thefilm is also seen in the location of the minimum in͗P2n͘. Large shifts in the location of the interface between regions of negative and positive magnetization are seen for tempera-tures between T*ϭ1.3and1.4.Mirroring this,a qualitative change in the profiles of͗P2n͘across thefilm also occurs between these temperatures.For T*Ͼ1.3the layer orienta-tional order parameter in the bulk of thefilm is small,and the minimum is located at the center of thefilm.Thus the para-magnetic phase of thefilm is associated with a delocalized interface between regions of positive and negative magneti-zation and an absence of orientational order away from the film surfaces.The ferromagnetic behavior of thefilm is as-sociated with interface localization within thefilm and the onset of nematic order in the center of thefilm.In a uniaxial liquid crystalfilm with competing surface fields,a sufficiently strong biquadratic interaction between the spins promotes orientational ordering within thefilm. This can give rise to interface localization in thefilm at tem-peratures above the critical temperature for the interface lo-calization transition in the corresponding anisotropic Heisen-bergfilm in whichϭ0.Thus the critical temperature characterizing the interface localization transition in a uniaxial liquid crystalfilm is a function of,⌳and D,i.e., T cϭT c(,⌳,D).Simulations have been performed to deter-mine͗P2͘and͗M z͘as functions of temperature for different values of the biquadratic coupling constantto study thedependence of T c(,⌳,D).Figures6͑a͒and6͑b͒show the results for one value of the bilinear exchange anisotropy,⌳ϭ0.1.The dependence of the critical temperature on⌳in similar models has been studied elsewhere͓6͔.As expected, the critical temperature T c(,⌳,D)is a monotonic increas-ing function offorfixed⌳and D.There is no spontaneous magnetic ordering for TϾT c,with͗M z͘ϭ0.For TϽT c, spontaneous ordering of thefilm is observed with͗M z͘Ͼ0. However,although͗M z͘decreases sharply to zero as T*→T c*,͗P2͘is a much more smoothly decreasing function of increasing T*,and͗P2͘Ͼ0even in the high temperature phase.This is a direct result of the symmetry of the layer orientational order parameter profile about the center of the film,which ensures a residual nonzero contribution to͗P2͘even in the isotropic phase due tofield induced order at the surfaces.In contrast,the antisymmetric magnetization profile of thefilm in the high temperature phase ensures͗M z͘ϭ0.Further information on the nature of the phase transition in thefilm can be obtained from the temperature dependence of the fourth-order cumulant of magnetization͓2,3,23͔:U Lϭ1Ϫ͗M4͘3͗M2͘2.͑11͒Forϭ0.5,Fig.7shows U L as a function of temperature for three different lattice sizes of Lϭ8,16,and32.The charac-teristic shape of the curves in thefigure is consistent with a second-order phase transition͓23͔.The critical temperature T c for the paramagnetic-ferromagnetic phase transition can be estimated from the point of intersection of U L for differ-ent values of L.Unfortunately,a precise estimation of T c for the interface localization transition of thefilm is difficult.Since the points of intersection of U L are spread over a small,but significant,temperature range.Similar observa-tions for U L have been reported for interface localization transition in thin Isisngfilms by Binder and co-workers͓2,4͔.From the results of Fig.7,the critical temperature forϭ0.5and⌳ϭ0.1is T c*ϭ1.660Ϯ0.005,this estimate being obtained from an average of the intersection points of resultsfor different L.The value of T c obtained from U L is in goodagreement with the temperature for which͗M z͘→0in Fig. 6͑a͒.This indicates that the critical temperatures for the other values ofcan be directly estimated from the temperatures for which͗M z͘→0in a plot of͗M z͘vs T*.The determi-nation of a more precise estimate for T c is beyond the scope of this paper.One interesting feature of Fig.6͑a͒is that forϭ5.0, where the system is dominated by the biquadraticexchange FIG.6.Temperature dependence of thefilm orientational order parameter͗P2͑͘open symbols͒and the z component of the magne-tization per spin͗M z͑͘solid symbols͒for⌳ϭ0.1with͑a͒ϭ0.5,2.5,and5.0and͑b͒ϭ2.7,3.0,and4.0.516PRE61HYUNBUM JANG AND MALCOLM J.GRIMSONinteraction,there is no longer a single phase transition in the film.The temperature at which magnetic order disappears differs markedly from the temperature at which orientational order disappears.This would suggest that for T *Ͻ3.9the film displays a ferromagnetic order,while for T *Ͼ5.9the system is in a paramagnetic isotropic state.But for 3.9ϽT *Ͻ5.9the system displays nematic order without any magnetic order.Such a polar phase was previously observed in studies of bulk uniaxial liquid crystals by Biscarini et al.͓15,16͔.However,for р2.5there is only a single phase transition.Systems with a pair of phase transitions and inter-mediate polar phase only appear for Ͼ2.5.Further results of ͗P 2͘and ͗M z ͘as a function of temperature are shown in Fig.6͑b ͒for three different values of in the range 2.5ϽϽ5.0.For ϭ2.7,the two separate magnetization and nem-atic ordering transitions are distinct,but only with a small difference in the critical temperatures associated with the two transitions of ⌬T c Ϸ0.1.As increases further,⌬T c in-creases smoothly with ⌬T c Ϸ0.3for ϭ3.0,⌬T c Ϸ1.0for ϭ4.0,and ⌬T c Ϸ2.0for ϭ5.0.The parameter values used in Fig.6͑a ͒were chosen to provide a direct comparison with the cluster Monte Carlo simulations by Biscarini et al.͓15,16͔of a bulk uniaxial liq-uid crystal with the Krieger-James Hamiltonian ͑1͒.Most remarkably the interface localization temperatures of the film found in this work are essentially the same as the bulk criti-cal temperatures obtained by Biscarini et al.In thick ferro-magnetic films,the interface localization transition is coinci-dent with the bulk critical temperature of the film.But for the film sizes used in this work,the anisotropic Heisenberg film with ϭ0show marked differences between the interface localization temperatures and the bulk critical temperatures for all ⌳.Similar observations have also been made for thin Ising films of this size ͓2͔.Unfortunately,it is not possible to tell whether a reduction in film thickness for the uniaxial liquid crystal film would lead to a significant difference be-tween the interface localization and bulk critical tempera-tures,since for thinner films the identification of surface andbulk regions of the film becomes problematic.Clearly as →0,one would expect the interface localization temperature in a uniaxial liquid crystal film to differ from the bulk critical temperature.However a full investigation of the depen-dence of the interface localization temperature film and bulk critical temperature in the →0limit is beyond the scope of this work.Further information on the phase transition in the film can be obtained from the temperature dependence of the specific heat C ϭ(ץU /ץT )V where U is the energy of the system.The excess specific heat C *ϭ(C ϪC id )/k B ,where C idis the specific heat of an ideal gas,is obtained from the fluc-tuation of the energy throughout the course of the simulation ͓24͔.Figures 8͑a ͒and 8͑b ͒show C *(T )for the same system parameters as in Figs.6͑a ͒and 6͑b ͒,respectively.The figure shows a single peak in C v *centered on T *ϭ1.6for ϭ0.5,on T *ϭ3.0for ϭ2.5,and on T *ϭ3.1for ϭ2.7.The peak is more pronounced for large values of .However,forFIG.7.Fourth-order cumulant of magnetization U L vs tempera-ture for three different lattice sizes of L ϭ8,16,and 32,with ϭ0.5and ⌳ϭ0.1.FIG.8.Temperature dependence of the reduced heat capacity C *for ⌳ϭ0.1with ͑a ͒ϭ0.5,2.5,and 5.0and ͑b ͒ϭ2.7,3.0,and 4.0.PRE 61517SURFACE-INDUCED ORDERING IN THIN UNIAXIAL ...。
供应链物流管理专业词汇整理
Chapter11.supply chain management 供应链管理2.zero defect 零缺陷3.perfect order 完美订单4.six-sigma performance 六西格玛管理体系5.marketing channel 营销渠道6.economic value 经济价值7.economy of scale 规模效益8.market value 市场价值9.trade—off 背反关系rmation sharing paradigm 信息共享模式11.process specialization paradigm 过程专业化模式12.electronic data interchange（EDI）电子信息交换13.made to plan（MTP）根据计划推测生产14.lead—time 交货期15.made to order(MTO)根据订单生产16.logistic outsourcing 物流外包17.stock keeping unit（SKU)库存单位18.integrated service provider（ISP）一体化服务供应商19.public warehouse公共仓库20.value—added service 增值服务21.third-party service provider 3PL 第三方物流服务供应商22.fourth—party service provider 4PL 第四方物流服务供应商23.anticipatory business model(push）预测性商业模式24.responsive business model（pull)快速响应型商业模式25.logistics postponement 物流延迟26.cash—to—cash conversion 现金转化周期27.dead net pricing 完全净价28.cash spin 现金周转29.operational performance 运作绩效30.order processing 订单处理31.customer accommodation 市场分销Chapter2 Inbound logistics 采购运筹，进口物流1。
Distributional torsion of charged domain walls with spin
a r X i v :g r -q c /9811017v 1 5 N o v 1998Distributional Torsion of Charged Domain WallsWith Spin DensitybyL.C.Garcia de AndradeDepartamento de F´ısica Te´o rica –IF –UERJ Rua S˜a o Francisco Xavier,524Cep 20550-003,Maracan˜a ,Rio de Janeiro,RJ,Brasil Electronic mail address:garcia@symbcomp.uerj.br Abstract An exact solution of Einstein-Cartan-Maxwell (ECM)field equations representing a charged domain wall given by the jump on the electric charge and spin density across the wall is obtained from the Riemannian theory of distributions.The Gauss-Coddazzi equations are used to show that spin,charge and Cartan torsion increases the repul-sive character of the domain wall.Taub and Vilenkin walls are discussed as well as their relations to wormhole geometry.The electric and torsion fields are constants at the wall.Key-Words:Einstein-Cartan Gravity and Domain Walls.PACS numbers:0420,0450I IntroductionThe motivation for the investigation of the domain walls[1]evolution stems for infla-tionary universes[2].The physical motivation to investigate charged domain walls[3]and domain walls with spinning particles[4][5]were provided mainly through the works of C.A. Lopez[3,5]andØ.Grøn[4]in their study of repulsive gravitationalfields[6,7].Their phys-ical motivation was basic to build electron models extending on Lorentz stress to General Relativity(GR).Since Hehl et al[8]have shown that Cartan torsion is the geometrical interpretation of spin of the particles this provides a natural motivation for the study of spinning particles in charged domain walls.Therefore here I shall be concerned with an exact static solution of ECM-field equations representing a charged planar domain wall endowed with particles with spin.The Einstein cosmological constant although it is one of the responsibles for the repulsive gravitation[9][7]is absent here.In fact the spin energy density plays the role of a“cosmological constant”on a sort of torsion vacuum.Here we use the fact discovered recently by myself and Lemos[10]that in EC-gravity space-time defects can be dealt with simply by substitution of the energy density and pressures by effective quantities with the contribution of spin energy densities.This allow us to reach a series of interesting physical conclusions concerning the gravitationally repulsive character[11]of domain walls as well as the horizon position in relation to the planar wall.This paper in a certain extent completes and generalizes my previous works on torsion walls[12,13].In section II we review ECM theory and apply in the case of static Taub[14]wall.It is important to note that Taub wall in the context of General Relativity(GR)is the well known no wall since(σ=p=0)whereσand p are respectively the energy density and the longitudinal pressure.This situation is not trivial in EC-gravity sinceσeff≡(σ−2πS2)and p eff≡p−2πS2vanishing do not imply thatσ=0=p.This is an important different between our paper and the others dealing with domain walls in(GR).In section III some consequences of Section II as the investigation of repulsive gravitation in(EC)-gravity are found.II Einstein-Cartan-Maxwell Gravitational Fields and Electrostatic Domain WallsLet us consider the formulation of ECM-field equations as given in Tiwari and Ray[14]. The main difference is that here we use(TR)-equations with plane symmetry while in the TR-paper their solution is spherically symmetric.In general the ECM-equations in the quasi-Einsteinian form maybe written asG b a({})=−8πeff T b a(1)which corresponds toG00({})=−2µzz−3µ2z+2µzνz=8π[σ+σE−2πS2]δ(z)e2ν≡8πσeffδ(z)(2) G22({})=G33({})=−µzz−µ2zz−νzz=−8π[σE−2πS2]e2νδ(z)=−8πp eff||e2νδ(z)(3) G11({})=−(µzνz+µ2z)=8π[p eff]δ(z)e2ν=8π[p⊥](σE+2πS3)](4)||Here{}represents the Riemannian connectionδ(z)is the Diracδ-distribution and where we have taken the Taub[15]plane symmetric space-time asds2=e2ν(−dt2+dz2)+e2µ(dx2+dy2)(5)and we have also considered S023≡u0S23as the only nonvanishing component of the spin density tensor and u0is the zero-velocity of the four-velocity.Here S23is the spin angular momentum tensor.In(GR)the orthogonal pressure p⊥vanishes.But here what vanishes is the effective orthogonal pressure in(4)p eff⊥≡0→p⊥=(σE+2πS2)(6) where hereσE≡E2/8πis the electrostatic surface energy density.Since torsion does not couple with the electrostaticfield[16]the Maxwell equations are the same as in(GR).In our case we take the electric and torsionfields as constants at the charged domain wall. Thus a simplyfirst integration of the system of(ECM)-differential system reads1µ+z=−−4µ+z=8πeff e2ν(8)2µ+z−2ν+z=−8πp eff e2ν(9) Now the Taub[15]wal is defined in EC-gravity as=0(10)σeff=p eff||which from(6)yieldsσE=+2πS2(11) or E2=16π2S2which impliesE=±4πS(12) Where the plus sign denotes the upper half Minkowski space-time.The non-Riemannian space-time deffect here is obtained by gluing together two half Minkowski spaces across spin-torsion-charge function.Where the result(11)comes from classical electrostatics[17]is the electrostaticfield at the plane.√Therefore the spin density squared S≡√by substitution of the RHS of(2)into(16)one obtains thefinal“Vilenkin”charged domain wall with spin and torsione2ν=e−µ 1−[4πσ+E2+8πS2]|z| (17) where E+=4π0σE is the electrostaticfield on upper half of the planar wall.Notice that the gravitational potential g00in(17)is written in terms of the electrostatic potential when the weakfield limit is taken.We may write the whole energy density asσeff=σ+2σE+2πS2.III Gravitational Repulsion of the Charged Domain Wall With Spin and TorsionIn this Section I shall review the Riemannian Gauss-Coddazzi equations given in Ipser and Skivie[11].Since the only modification of charged spinning particles domain wall is the introduction of spin and electric surface charge densities into the effective energy densities,the modification of physical conclusions of(ECM)-domain walls is basically due to the changes in the densities.Before the examination of the Gauss-Codazzi eqns.let us consider thefirst important physical change due to the introduction of spin,torsion and the electrostaticfield into the domain wall.Thefirst change is obvious from the metric (17)and is given by the“new horizon”singularityg00= 1− 4πσ+E2+8π2S2 |z| −1/2→∞(18) whereσeff=σ+2σE+2πS2(19) yielding|z|=1A similar situation appears in the case of the cosmological constant in the case of plane symmetric exact solution of Einstein equations.Since thefirst term on the RHS of(21)is positive if E>0,σ<0which reminds us of the wormwhole geometry[18].Let us now turn to the Gauss-Coddazzi equations3R+ππij−π2=−2G ijξiξj(21)ijh ij D KπjK−D iπ=G jK h j iξK(22) where3R is the Ricci scalar curvature of the3-dimensional geometry h ij of the surface S,π≡πi i where.πij≡D iξj=πji(23) is the extrinsic curvature andD i≡h j i∇j(24) is the covariant derivative projected onto the surface S and h ij≡g ij−ξiξj is the3-dimensional geometric metric tensor.From the above eqns,Ipser and Skivie[11]were able to deduce the equation for the acceleration of a test particle offthe wallξi u j∇jξi|+=−ξi u j∇jξi|−=2πG N(σeff−2p eff)(25)into where G N is the Newtonian gravitational constant.By substitution ofσeff and p eff||the eq.(26).ξi u j∇jξi|+=2πG N(σ+σE−2πS2−2σE+4πS2)=2πG N(σ−σE+2πS2)(26) Since one knows that an observer who wishes to remain stationary next to the wall must accelerate away from the wall if(σeff−2p eff||)>0and towards to the wall if (σeff−2p eff||)<0one notes from(27)that repulsive domain wall would haveσ<σE−2πS2(27) Since in most of the physical systems in nature the spin energy density2πS2is never higher than the surface electrostatic energy densityσE,σis not necessarily negative. Nevertheless for attractive domain wallsσ>σE−2πS2>0(28)and the stress-energy surface domain wall density should not violate the weak energy condition,then the wormhole geometry is not possible in this case.Other applications of charged domain walls with spin and torsion maybe found else-where.In particular a detailed account of the relation between domain walls in EC-gravity and traversable wormholes maybe found in recent paper by myself and Lemos[10]. Also recently other type of topological defect(cosmic strings)have been investigated by Cl´e ment[21]as a source offlat wormholes.Finally it is important to mention that the matching conditions in EC-theory were not necessary to deal with the non-Riemannian domain walls[22]discussed here.Distributional curvature of cosmic strings has been recently investigated by Wilson[23].AcknowledgementsI am very much indebt to P.S.Letelier,Prof. C.A.Lopez and A.Wang for helpful discussions on this subject of this paper.Some suggestions of an unknown referee are gratefully acknowledged.Grants from CNPq(Ministry of Science of Brazilian Govern-ment)and Universidade do Estado do Rio de Janeiro(UERJ)are acknowledged.References[1]A.Vilenkin and P.Shellard,Cosmic strings and other topological defects(1994),monographs,in mathematical physics,Cambridge University Press.[2]Ø.Grøn,Am.J.Phys.54(1986),46.[3]C.A.Lopez,Phys.Rev.D38(1988)3662.[4]Ø.Grøn,Phys.Rev.D31(1985),2129(Brief Reports).[5]C.A.Lopez,Phys.Rev.D30(1984)313.[6]C.A.Lopez,Gen.Rel.and Grav.(1997).[7]P.A.Amundsen andØ.Grøn,Phys.Rev.D27(1983),1731.[8]F.W.Hehl,J.D.McCrea,E.Mielke and Yuval Ne’eman,Phys.Reports(1995),July.[9]J.Ponce de Leon,J.Math.Phys.29,(1)(1988),197.[10]L.C.Garcia de Andrade and J.P.S.Lemos,Topological Defects:Domain walls withspin and torsion and wormhole geometry(1988)-DFT internal reports.[11]J.Ipser and p.Skivie,Phys.Rev.D30,4,(1984)712.[12]L.C.Garcia de Andrade,J.Math.Phys.(1988)39,Jan.issue.[13]L.C.Garcia de Andrade,Mod.Phys.Lett.A,(1997)27,12,2005.[14]R.N.Tiwari and S.Ray.Gen.Rel.and Grav.(1997),29,6,683.[15]A.Taub,J.Math.Phys.21(1980),1423.[16]F.W.Hehl,Found.Phys.(1985),15,451.[17]J.D.Jackson,Classical Electrodynamics(1970)Wiley&Sons.[18]M.Visser,Lorentzian wormholes:from Einstein to Hawking,(1996),AIP press.[19]O.Ventura,MSc.Thesis,(1994),Observat´o rio Nacional(ON-CNPq),in portuguese.[20]J.P.S.Lemos and O.Ventura,J.Math.Phys.(1994).[21]G.Cl´e ment,J.Math.Phys.38,(11)(1997),5807.[22]L.C.Garcia de Andrade,On non-Riemannian domain walls,(1998)-DFT-UERJ-internal reports.[23]J.Wilson,Class.Quantum Grav.,14,(1997)3337.。
物理专业 词汇S2
specific conductance 导电率
specific electronic charge 电子的比电荷
specific gravity 比重
specific gravity bottle 比重瓶
specific heat 比热
spectroscopic parallax 分光视差
spectroscopic photography 分光摄影术
spectroscopy 光谱学
spectrum 光谱
spectrum locus 光谱轨迹
spectrum selector 光谱选挥器
spectrum variable 光谱变星
source of light 光源
source of sound 声源
south pole 南极
space 空间
space astronomy 空间天文学
space charge 空间电荷
space charge density 空间电荷密度
space charge effect 空间电荷效应
spectrohelioscope 太阳光谱观测镜
spectrometer 光谱仪
spectrometry 光谱测定法
spectrophotofluorometer 荧光分光光度计
spectrophotography 光谱摄影学
spectrophotometer 分光光度计
spectrophotometry 光谱测定法
spark chamber 火花室
spark counter 火花计数器
磁共振的英文缩写
磁共振的英文缩写MRI：Magnetic Resonance Imaging磁共振成像NMRI：Nuclear Magnetic Resonance Imaging核磁共振成像MRA：Magnetic Resonance Angiography磁共振血管造影CE-MRA：contrast enhanced magnetic resonance angiography对比增强磁共振血管成像MRV：Magnetic Resonance Venography磁共振静脉造影VW-MRI：vessel wall magnetic resonance imaging磁共振血管壁成像MRCP：Magnetic Resonance cholangiopancreatography磁共振胰胆管成像MRM：Magnetic Resonance Myelography磁共振脊髓成像MRU：Magnetic Resonance urography磁共振尿路成像MRN：Magnetic Resonance neurography磁共振神经成像CMR：Cardiovascular MR心血管磁共振检查技术fMRI：functional magnetic resonance imaging磁共振功能成像MRE：Magnetic Resonance Elastography磁共振弹性成像T1WI：T1-weighted imagingT1加权成像T2WI：T2-weighted imagingT2加权成像PDWI：proton density weighted imaging质子密度加权成像EPI：echo planar imaging平面回波成像MS-EPI：multi shot echo planar imaging多激发平面回波成像DWI：diffusion weighted imaging扩散加权成像(小视野弥散Philips-ZOOM/Siemens-ZOOMit/GE-FOCUS)ADC：apparent diffusion coefficient表观扩散系数DWIBS：diffusion weighted imaging with background suppression背景抑制扩散加权成像RESOLVE：readout segment of long variable echo trains 基于读出方向分段K空间的多次激发弥散加权成像(Siemens)MUSE：multi-slab parallel EPI多激发节段式EPI采集空间信号敏感性编码图像重建(GE)DTI：diffusion tensor imaging扩散张量成像PWI：perfusion weighted imaging灌注加权成像BOLD：blood oxygenation level dependent血氧水平依赖RF：Radio Frequency射频TR：repetition time重复时间TE：echo time回波时间(Effective TE有效TE)Minimum TE：部分回波技术TI：inversion time反转时间ES：echo space回波间隙ETL：echo train length回波链长度BW：bandwidth带宽FA：flip angle反转角TA：Acquisition time采集时间NA：number of acquisitions采集次数NSA：number of signal averaged信号平均次数NEX：number of excitation激励次数TD：time of delay延迟时间WFS：water fat shift水脂位移FC：flow pensation流动补偿TOF：time of flight时间飞跃TRICKS：time resolved imaging of contrast Kinetics对比剂动态成像PC：phase contrast相位对比VENC：velocity encoding流速编码NPW：no phase wrap去相位卷褶IR：inversion recovery反转恢复MT：magnetization transfer磁化转移(磁化传递)FT：fourier transform傅里叶变换VPS：Views Per Segment每段视图BSP TI：blood suppression TI血夜抑制反转时间(IFIR参数)序列SE：spin echo自旋回波FSE：fast spin echo快速自旋回波TSE：turbo spin echo快速自旋回波FRFSE：fast recovery fast spin echo快速恢复快速自旋回波(GE)TSE-Restore：快速恢复快速自旋回波(Siemens)TSE DRIVE(TSE driven equilibrium DE驱动平衡)：快速恢复快速自旋回波(Philips)SSFSE：single shot fast spin echo单次激发快速自旋回波HALF-SS-TSE：half-fourier acquisition single-shot turbo spin echo半傅里叶单次激发快速自旋回波(Philips)HASTE：half-fourier acquisition single-shot turbo spin echo半傅里叶单次激发快速自旋回波(Siemens)FLAIR：fluid attenuated inversion recovery水抑制反转恢复ASL：arterial spin labeling动脉自旋标记BPAS：basi-parallel anatomical scanning平行椎基底动脉系统扫描FIR：fast inversion recovery快速反转恢复(TIR：turbo inversion recovery)DIR：dual inversion recovery(有资料译为double inversion recovery)双重反转恢复下面三个技术（VISTA/CUBE/SPACE）摘自懋氏百科全书，后面两个的中文是我瞎翻译的：VISTA(3D VIEW)：volume isotropic turbo spin echo acquisition各向同性快速自旋回波容积采集(Philips)CUBE：3D fast spin echo with an extended echo train acquisition长回波链3D快速自旋回波采集(GE)SPACE：sampling perfection with application optimized contrast using different flip angle evolution最优可变翻转角改善对比完美采样(Siemens)梯度回波GRE：gradient recalled echo梯度回波(GE)FFE：fast field echo快速场回波(Philips)GE：gradient echo梯度回波(Siemens)TFE：turbo field echo超快速场回波FISP：fast imaging with steady-state precession稳态进动快速成像(Siemens)PSIF(Siemens)：采集刺激回波的GRE序列；在时序上与FISP 相反遂命名为PSIF(Philips为T2-FFE；GE为CE-GRASS:contrast enhanced GRASS)DESS：dual spin steady state双回波稳态进动(Siemens独有3D序列，显示软骨优势；同时采集FISP信号和PSIF信号)MEDIC：multiple echo data image bination多回波数据合并成像(Siemens)MERGE：multiple echo recalled gradient echo多回波梯度回波 (GE 2D)COSMIC：coherent oscillatory state acquisition for the manipulation imaging contrast连续振荡状态采集操控成像对比(GE 3D多回波合并成像)mFFE(Philips多回波)：multiple fast field echoSWI：susceptibility weighted imaging磁敏感加权成像QSM：quantitative susceptibility mapping定量磁化率成像SSFP：steady state free precession普通稳态自由进动(GE 的GRE、Fast GRE均属该类型；西门子为FISP；在飞利浦上称为conventional FFE)Balance-SSFP：balance steady state free precession平衡式稳态自由进动(Philips)FIESTA：fast imaging employing steady stateacquisition稳态采集快速成像(GE)FIESTA-C：FIESTA-cycled phases双激发稳态采集快速成像(GE)True FISP：true fast imaging with steady state precession真稳态自由进动快速成像(Siemens)CISS：constructive interference in the steady state稳态进动结构相干(双激发)B-FFE：balance fast field echo平衡式快速场回波(Philips)TRANCE：triggered angiography non-contrast enhanced触发血管造影非对比增强(Philips; Siemens为 Native truefisp; GE为IFIR: InFlow Inversion Recovery)QISS：Quiescent-Interval Single-Shot MR血管造影-静态间隔单次激发成像是一种用于外周MRA的非增强MRA技术(Siemens)。
李政道诺贝尔领奖辞lee-lecture.pdf
The interactions (not including the gravitational forces) between these par-ticles can be classified into three distinct groups:1. Strong Interactions. This group is responsible for the production and thescattering of nucleons, pions, hyperons (i.e. etc.) and K mesons. It ischaracterized by a couplinggC> = (1/137).3.Weak Interactions. This group includes all known non-electromagnetic de-cay interactions of these elementary particles and the recently observed ab-sorption process of neutrinoes by nucleons2.These interactions are charac-terized by coupling constants1957 T.D.L E EFig. 2.YThe law of conservation of parity is valid for both the strong and the elec-tromagnetic interactions but is not valid for the weak interactions. Today’s discussions will be mainly on the recently observed effects of nonconserva-tion of parity in the various weak interactions.IIThe weak interactions cover a large variety of reactions. At present there are about 20 known phenomenologically independent reactions ranging from the decay of various hyperons to the decay of light particles. Within the last year, many critical experiments have been performed to test the validity of the law of conservation of parity in these reactions. We shall first summarize the experimental results together with their direct theoretical implications.Next, we shall discuss some further possible consequences and theoretical considerations.W E A K I N T E R A C T I O N S A N D P A R I T Y M i r r o r r e f l e c t i o n409Fig. 3.(1)emitted, differentiates in a mostdirect way a right-handed system from a left-handed system. Thus the non-conservation of parity or the non-invariance under a mirror reflection can be established without reference to any theory.Furthermore from the large amount of angular asymmetry observed itcan also be established 4that the (1)in which each particle is described by a quantized wave equation. In partic-ular the neutrino is described by the Dirac equation6are the four (4 × 4)anti-commuting Dirac matrices and= ict are the four space-time coordinates. For each given mo-mentum there exists two spin states for the neutrino and two spin states for the anti-neutrino. These may be denoted by If we define thehelicity H to bewith the unit vector along the momentum direc-tion, then these four states have, respectively, helicities equal to + I, - I, -I and + I (Fig. 4). M a thand a left-handed part=(6)andIt is easy to see that both separately satisfy the Dirac equationt s ecomposition the β process of a nucleus A can be rep-[Eq. (2)]. With hi dresented schematically asFig. 4.and and+(7’)(8’)with as the corresponding amplitudes for emission ofUnder the charge conjugation operator we change a particle to its anti-particle but we do not change its spatial or spin wave functions. Conse-quently it must have the same helicity. Thus, if the β-decay process is in-variant under the charge conjugation operator, then we should expect pro-cess (7) to proceed with the same amplitude as process (8’). The condition for invariance under charge conjugation is, thenz (9)for all i = S, T, V, P, A.In the decay of 60Co, because there is a difference of spin values between 6O Co and 60Ni, only the terms i = T and i = A contribute. From the large angular-asymmetry observed it can be safely concluded that for bot h i = T, Awhich contradicts Eq. (9)and proves the non-invariance of β-interaction under charge conjugation. For illustration purposes, we assume in the abovethe neutrino to be described by a 4-component theory and further we assume that in the412 1957T.D.L E ERecently many more experiments7 have been performed on the longi-tudinal polarization of electrons and positrons, th e β−γ, correlation together with the circular polarization of the γ radiation and the β angular distribu-tion with various polarized nuclei other than 60Co. The results of all these experiments confirm the main conclusions of the first 60Co experiment, that both the parity operator and the charge conjugation operator are not con-served in β-decay processes.Another interesting question is whether the β-decay interaction is invariant under the product operation of (charge conjugation x mirror reflection). Under such an operation we should compare the decay of A with that ofa n dd e c a yThe π± meson decays into a µ± meson and a neutrino. The µ± meson, in turn, decays into an e± and two neutrinoes (or anti-neutrinoes). If parity is not conserved in π-decay, the µ meson emitted could be longitudinally po-Fig. 5.WEAK INTERACTIONS AND PARITY413 larized. If in the subsequentmeson (Fig. 5). Consequently in themeson measured in the rest system of measured in the restsystem ofThe experimental results8 on these angular correlations appeared within a few days after the results onLater, direct measurements9 on the longitudinal polarization of the posi-tron fromdecayIn this case we have instead of themeson and a neutrino (Fig. 6). Experiment10 on the angular correlation between theestablishes that in K-decay the par-ity as well as the charge conjugation operator is not conserved.(4)on proton. TheFig. 6.subsequently decays into a proton plus aπ− (Fig. 7). The observation of an a symmetrical distribution with respect to the sign of the product(Ginx the mo-mentum of the lambda particle,,,,,and that of the decay pionandFurthermore, from the amount of the large up-down asymmetry it can be concluded that the Λο-decay interaction is also not invariant under the charge conjugation operation.From all these results it appears that the property of nonconservation of parity in the variou s weak interactions and the noninvariance property of these interactions under charge conjugation are well established. In connec-tion with these properties we find an entirely new and rich domain of nat-ural phenomena which, in turn, gives us new tools to probe further into the structure of our physical world. These interactions offer us natural ways to polarize and to analyze the spins of various elementary particles. Thus, for example, the magnetic moment of the µ meson can now be measured to an extremely high degree of accuracy12which, otherwise, would be unattain-W E A K I N T E R A C T I O N S A N D P A R I T Y415 able; the spins of some hyperons now may perhaps be determined13 un-ambiguously through the observed angular asymmetries in their decays; new aspects of the electromagnetic fields of various gas, liquid and solid materials can now be studied by using these unstable, polarized particles. However, perhaps the most significant consequences are the opening of new possibil-ities and the re-examination of our old concepts concerning the structure of elementary particles. We shall next discuss two such considerations - the two-component theory of neutrino, and the possible existence of a law of con-servation of leptons.IIIBefore the recent developments on nonconservation of parity, it was cus-tomary to describe the neutrino by a four-component theory in which, as we mentioned before, to each definite momentum there are the two spin states of the neutrino plus the two spin states of the antineutrinoIn the two-component theory, however, we assume two of thesestates, say, simply do not exist in nature. The spin of the neutrinois then always parallel to its momentum while the spin of the antineutrino is always antiparallel to its momentum. Thus in the two-component theory we have only half of the degrees of freedom as in the four-component the-ory. Graphically we may represent the spin and the velocity of the neutrino by the spiral motion of a right-handed screw and that of the antineutrino by the motion of a left-handed screw (Fig. 8).The possibility of a two-component relativistic theory of a spin ½ particle was first discussed by H. Weyl14 as early as 1929. However, in the past, be-cause parity is not manifestly conserved in the Weyl formalism, it was always rejected15.With the recent discoveries such an objection becomes com-pletely invalid16.To appreciate the simplicity of this two-component theory in the present situation it is best if we assume further the existence of a conservation law for leptons17. This law is in close analogy with the corresponding conserva-tion law for the heavy particles. We assign to each lepton a leptonic num-ber l equal to +1or -1and to any other particle the leptonic number zero. The leptonic number for a lepton must be the negative of that for its antiparticle. The law of conservation of leptons then states that « in all physical processes the algebraic sum of leptonic numbers must be con-served ».W E A K I N T E R A C T I O N S A N D P A R I T Y417 two-component theory we have to investigate in detail all the neutrino pro-cesses. For example inor4181957T.D.L E E1. C. N. Yang, Nobel Lecture, this volume, p. 393.2. C. L. Cowan, Jr., F. Rines, F. B. Harrison, H. W. Kruse, and A. D. McGuire,Science, 124 (1956) 103.3. C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson,Phys.Rev., 105 (1957) 1413.4. T. D. Lee, R. Oehme, and C. N. Yang, Phys. Rev., 106 (1957) 340; B. L. Ioffe, L.B. Okun, and A. P. Rudik, J.E.T.P. (U.S.S.R.), 32 (1957) 396.5. We remark here that if the neutrino is described by a two-component theory (seeSection III) then the result of the large angular asymmetry in60Co decay estab-lishes in a trivial way the non-Invariance property of β-decay under the charge conjugation operation. However, this non-invariance property can also be provedunder a much wider framework. In this section we take as an example the case ofa four-component theory of neutrino to illustrate such a proof6.For notations and definitions of γmatrices see, e.g., W. Pauli,Handbuch der Physik,Julius Springer Verlag, Berlin, 1933, Vol. 24.7. For a summary of these experiments see, e.g., Proceedings of the Seventh AnnualRochester Conference,Interscience, New York, 1957.8. R. L. Garwin, L. M. Lederman, and M. Weinrich,Phys. Rev., 105 (1957) 1415;J. I. Friedman and V. L. Telegdi,Phys. Rev., 105 (1957) 1681.9. G. Culligan, S. G. F. Frank, J. R. Holt, J. C. Kluyver, and T. Massam, Nature, 180(1957) 751.10. C. A. Coombes, B. Cork, W. Galbraith, G. R. Lambertson, and W. A. Wenzel,Phys. Rev., 108 (1957) 1348.11. J. Crawford, et. al., Phys. Rev., 108 (1957) 1102; F. Eisler et al.,Phys. Rev., 108(1957) 1353; R. Adair and L. Leipuner, Phys. Rev., (to be published).12. T. Coffin, R. L. Garwin, L. M. Lederman, S. Penman, and A. M. Sachs, Phys.Rev., 107 (1957) 1108.13. T. D. Lee and C. N. Yang, Phys. Rev., 109 (1958) 1755.14. H. Weyl, Z. Physik, 56 (1929) 330.15. Cf. W. Pauli, Handbuch der Physik, Julius Springer Verlag, Berlin, 1933, Vol. 24,pp. 226-227.16. The possible use of a two-component theory for expressing the nonconservationproperty of parity in neutrino processes was independently proposed and dis-cussed by T. D. Lee and C. N. Yang, Phys. Rev., 105 (1957) 1671; A. Salam, Nuovo Cimento, 5 (1957) 299; and L. Landau,Nucl. Phys., 3 (1957)127.17. The possible existence of a conservation law for leptons has been discussed beforethe discovery of nonconservation of parity. Cf. E. Konopinski and H. M. Mah-moud, Phys. Rev., 92 (1953) 1045.。
order知识点总结
order知识点总结IntroductionOrder is an important concept in various domains, including business, economics, mathematics, and sociology. It is the arrangement or organization of elements, often following a specific pattern or rule. Understanding order is crucial for efficiency, productivity, and harmony in a variety of settings. In this article, we will explore various aspects of order, its importance, and its applications in different fields.Types of OrderOrder can be categorized into various types based on the context in which it is used. Some common types of order include:1. Numerical Order: This type of order deals with the arrangement of numbers in ascending or descending sequence. It is commonly used in mathematics and statistics.2. Chronological Order: Chronological order refers to the arrangement of events or items in the order in which they occurred or were created. It is often used in historical narratives, timelines, and project planning.3. Alphabetical Order: Alphabetical order involves the arrangement of items based on their initial letters, following the sequence of the alphabet. It is commonly used for organizing lists of names, titles, and other information.4. Spatial Order: Spatial order refers to the arrangement of items or elements based on their physical location or position. It is often used in geography, architecture, and design.5. Logical Order: Logical order involves the arrangement of elements based on a logical sequence or structure. It is commonly used in problem-solving, decision-making, and argumentation.Importance of OrderOrder plays a crucial role in various aspects of life and society. Some of the key reasons why order is important are:1. Organization: Order provides a systematic and structured way of organizing elements, which helps in making sense of complex information and processes.2. Efficiency: Orderliness leads to efficiency by reducing the time and effort required to find or access information, resources, or materials.3. Clarity: Order makes it easier to understand and communicate information, ideas, and instructions, leading to clarity and precision in various activities.4. Productivity: A well-ordered environment fosters productivity by minimizing distractions, confusion, and wastage of resources.5. Stability: Order contributes to stability and predictability in systems and societies, which is essential for their functioning and development.Applications of OrderOrder is applied in various fields and disciplines for different purposes. Some common applications of order include:1. Business and Management: In business and management, order is essential for organizing work processes, managing resources, and maintaining productivity.2. Education: Order is important in educational settings for structuring curricula, organizing learning materials, and maintaining discipline in classrooms.3. Law and Justice: Order is crucial in legal systems for ensuring fairness, adherence to rules, and the administration of justice.4. Science and Technology: In scientific research and technological development, order is fundamental for organizing data, conducting experiments, and developing systems and structures.5. Arts and Design: Order plays a significant role in the arts and design fields, influencing the composition, aesthetics, and functionality of various creations.Order in MathematicsIn mathematics, order is a fundamental concept with diverse applications. Some key aspects of order in mathematics include:1. Ordering Numbers: Numbers can be ordered in ascending or descending sequence based on their value. This is essential for comparing, ranking, and organizing numerical data.2. Order of Operations: The order of operations in mathematics specifies the sequence in which different mathematical operations (e.g., addition, subtraction, multiplication, division) should be performed within an expression or equation.3. Order Relations: Order relations define the relationship between elements in a set based on their relative position or value. Examples include less than, greater than, equal to, and between relations.4. Ordered Pairs: In coordinate geometry, ordered pairs are used to represent the positionof points on a plane, with the x-coordinate indicating the horizontal position and the y-coordinate indicating the vertical position.5. Partial Order and Total Order: In set theory and abstract algebra, partial order and total order are important concepts that define the relationships between elements in a set with respect to a given order relation.Order in EconomicsIn economics, order is essential for understanding, analyzing, and influencing various economic phenomena. Some important aspects of order in economics include:1. Market Order: Market order refers to the arrangement of buying and selling transactions in financial markets, which determines the prices and quantities of traded assets.2. Economic Order Quantity (EOQ): EOQ is a concept in inventory management that determines the optimal order quantity for minimizing inventory holding costs and ordering costs.3. Order of Production: In production and supply chain management, the order of production refers to the sequence of manufacturing and assembly processes to optimize efficiency and minimize lead times.4. Order Flow: Order flow in financial markets represents the buy and sell orders received by market participants, which influence market liquidity, price movements, and trading strategies.5. Orderly Market: An orderly market is characterized by stability, transparency, and fair competition, which are essential for efficient resource allocation and investment decisions. Order in SociologyIn sociology, order is a central concept for understanding social structures, institutions, and interactions. Some key aspects of order in sociology include:1. Social Order: Social order refers to the stable patterns of social relationships, customs, and norms that regulate behavior and interaction within a society or community.2. Social Order Theory: Social order theories aim to explain the mechanisms and factors that contribute to the maintenance of social order, including institutions, values, and power dynamics.3. Order and Conflict: The relationship between order and conflict is a central theme in sociology, as social order can be disrupted or challenged by various forms of conflict, such as inequality, deviance, and revolution.4. Orderly Society: An orderly society is characterized by a strong social order, where individuals and groups adhere to shared norms, laws, and moral codes, leading to stability and cohesion.5. Order Maintenance: Social order maintenance involves the efforts of institutions, authorities, and communities to uphold and enforce rules, laws, and social norms to prevent disorder and conflict.ConclusionOrder is a fundamental concept that permeates various aspects of life, society, and the natural world. Understanding the different types of order, its importance, and its applications in different fields is essential for fostering efficiency, productivity, and harmony in diverse contexts. Whether in mathematics, economics, sociology, or other disciplines, order plays a vital role in shaping and organizing our experiences and interactions. By recognizing and appreciating the significance of order, we can better navigate and contribute to the complex systems and structures that govern our lives.。
Magnetic Ordering and Superconductivity in the RE$_2$Ir$_3$Ge$_5$ (RE = Y, La-Tm, Lu) Syste
Abstract
We report structure, electrical resistivity, magnetic susceptibility, isothermal magnetization and heat-capacity studies on polycrystalline samples of the intermetallic series RE2Ir3Ge5 (RE = Y, La, Ce-Nd, Gd-Tm, Lu) from 1.5 to 300 K. We find that the compounds for RE = Y, La-Dy, crystallize in the tetragonal Ibam (U2Co3Si5 type) structure whereas the compounds for RE= Er-Lu, crystallize in a new orthorhombic structure with a space group Pmmn. Samples of Ho2Ir3Ge5 were always found to be multiphase. The compounds for RE = Y to Dy which adopt the Ibam type structure show a metallic resistivity whereas the compounds with RE = Er, Tm and Lu show an anomalous behavior in the resistivity with a semiconducting increase in ρ as we go down in temperature from 300 K. Interestingly we had earlier found a positive temperature coefficient of resistivity for the Yb sample in the same temperature range. We will compare this behavior with similar observations in the compounds RE3Ru4Ge13 and REBiPt. La2Ir3Ge5 and Y2Ir3Ge5 show bulk superconductivity below 1.8 K and 2.5 K respectively. Our results confirm that Ce2Ir3Ge5 shows a Kondo lattice behavior and undergoes antiferromagnetic ordering below 8.5 K. Most of the other compounds containing magnetic rare-earth elements undergo a single antiferromagnetic transition at low temperatures (T≤12 K) while Gd2Ir3Ge5, Dy2Ir3Ge5 and Nd2Ir3Ge5 show multiple transitions. The TN ’s for most of the compounds
磁共振成像技术中英文名词对照
Chemical shift imaging ,CSI
化学位移成像
Diffusion tensor imaging ,DTI
集中张量成像
Diffusion weighted imaging ,DWI
集中加权成像
Echo planar imaging ,EPI
平面回波成像
Echo space ,ES
梯度回波
Gradient recalled echo–echo planar imaging,GRE-EPI
梯度回波平面回波成像
Half-fourior acquisition single-shot turbo spin Echo ,HASTE
半傅里叶收集单次激发快速自旋回波
Inversion recovery ,IR
持续性动脉自旋标识表记标帜
Contrast enhanced magnetic resonance angiography,CE-MRA
比较加强磁共振血管成像
Chemical shift selective saturation,CHESS
化学位移选择饱和
Contrast to noise ratio ,CNR
磁化预备快速梯度回波
Magnetization preparedrapid gradient echo imaging, MP-RAGE
磁化预备快速梯度回波成像
Magnetic resonance angiograghy ,MRA
磁共振血管成像
Magnetic resonance cholangiopancreatography,MRCP
矩形视野
Region of interest , ROI
2 Fermi Liquids and Luttinger Liquids
10
Heinz J. Schulz et al.
Subsequently, I will first briefly discuss the case of a noninteracting manyfermion system (the Fermi gas), and then turn to Landau’s theory of the interacting case (the liquid), first from a phenomenological point of view, and then microscopically. A much more detailed and complete exposition of these subjects can be found in the literature [5–9]. 2.2.1 The Fermi Gas
2
Fermi Liquids and Luttinger Liquids
Heinz J. Schulz, Gianaurelio Cuniberti, and Pierbiagio Pieri
2.1
Introduction
In these lecture notes, corresponding roughly to lectures given at the summer school in Chia Laguna, Italy, in September 1997, an attempt is made to present the physics of three-dimensional interacting fermion systems (very roughly) and that of their one-dimensional counterparts, the so-called Luttinger liquids (in some more detail). These subjects play a crucial role in a number of currently highly active areas of research: high temperature and organic superconductors, quantum phase transitions, correlated fermion systems, quantum wires, the quantum Hall effect, low-dimensional magnetism, and probably some others. Some understanding of this physics thus certainly should be useful in a variety of areas, and it is hoped that these notes will be helpful in this. As the subject of these lectures was quite similar to those delivered at Les Houches, some overlap in the notes [1] was unavoidable. However, a number of improvements have been made, for example a discussion of the “Klein factors” occurring in the bosonization of one-dimensional fermions, and new material added, mainly concerning spin chains and coupled Luttinger liquids. Some attempt has been made to keep references up to date, but this certainly has not always been successful, so we apologize in advance for any omissions (but then, these are lecture notes, not a review article).
英语作文中逻辑顺序有哪些
英语作文中逻辑顺序有哪些逻辑顺序在英语作文中非常重要，它可以帮助文章更加清晰地传达作者的观点和信息。
通常情况下，英语作文的逻辑顺序可以采用时间顺序、空间顺序、问题解决顺序、因果关系顺序等。
以下是一个范文，展示了逻辑顺序在英语作文中的应用：Title: Exploring the Various Logical Orders in English Composition。
Introduction:In the realm of English composition, logical order plays a pivotal role in crafting coherent and persuasive essays. Whether it's narrating a personal experience, analyzing a complex issue, or arguing a point, the arrangement of ideas significantly influences the effectiveness of communication. This essay delves into the exploration of various logical orders commonly employed in English composition, illustrating their significance through examples and analysis.Chronological Order:One of the most straightforward and commonly usedlogical orders in English composition is chronological order. This order arranges information based on the sequence of events, allowing readers to follow a clear timeline. For instance, when recounting a personal journey, such as a travelogue, chronological order helps innarrating the experiences in a systematic manner from the beginning to the end. It enables readers to visualize the progression of events and enhances the coherence of the narrative.Spatial Order:Spatial order, on the other hand, organizes information based on physical location or spatial arrangement. This logical order is particularly useful when describing scenes, settings, or objects. By structuring the composition according to spatial relationships, writers can createvivid imagery and immersive experiences for the readers.For example, in a descriptive essay about a picturesque landscape, spatial order allows the writer to guide the reader's imagination by detailing the arrangement of elements such as mountains, rivers, and forests.Problem-Solution Order:In essays addressing complex issues or challenges, the problem-solution order is often employed to present a logical progression of ideas. This order first outlines the problem or issue at hand, followed by proposed solutions or strategies for resolution. By presenting the problem andits solution in sequence, writers can effectively communicate the significance of the issue and advocate for specific actions. For instance, in an argumentative essay on environmental pollution, the problem-solution order allows the writer to elucidate the causes of pollution and propose mitigating measures for environmental conservation.Cause and Effect Order:Another prevalent logical order in English compositionis the cause and effect order, which elucidates the relationship between events or phenomena. This order identifies the causes that lead to certain effects or consequences, or conversely, examines the effects resulting from specific causes. By delineating causal relationships, writers can offer insights into the underlying mechanisms driving certain outcomes. For example, in an academic essay analyzing the economic recession, cause and effect order enables the writer to examine the factors contributing to the recession and its impact on various sectors.Conclusion:In conclusion, logical order serves as a fundamental principle in English composition, guiding the arrangement of ideas to enhance clarity, coherence, and persuasiveness. Whether employing chronological order, spatial order, problem-solution order, or cause and effect order, writers can effectively structure their compositions to engage readers and convey their message with precision. By mastering the art of logical ordering, writers can elevatethe quality of their essays and effectively communicate their ideas to a wider audience.。
门店设计缺点英语作文
门店设计缺点英语作文Title: Flaws in Store Design: A Critical Analysis。
In the contemporary retail landscape, the design of physical stores plays a pivotal role in attracting and retaining customers. However, despite the emphasis on creating engaging and functional spaces, there are often inherent flaws in store designs that hinder their effectiveness. This essay aims to explore some common drawbacks in store design and their implications.Firstly, one prominent issue is poor spatial planning. Many stores fail to optimize their layout to facilitate smooth customer flow and easy navigation. This can result in congestion, particularly during peak hours, leading to frustration among shoppers. Additionally, inadequate spacing between aisles and displays can create a cramped atmosphere, diminishing the overall shopping experience. Moreover, a cluttered layout makes it challenging for customers to locate products efficiently, impacting salesand customer satisfaction negatively.Secondly, the lack of attention to aesthetic appeal is another significant flaw observed in store designs. While functionality is crucial, aesthetics also play a vital role in shaping customers' perceptions and emotions. Stores with uninspiring or outdated decor fail to captivate the attention of modern consumers who seek immersive and visually stimulating experiences. Furthermore, inconsistent branding elements or mismatched themes can dilute thestore's identity, making it less memorable and distinctive in the competitive retail landscape.Thirdly, insufficient consideration for accessibility poses a fundamental flaw in many store designs. Accessibility encompasses not only physical access for individuals with disabilities but also considerations for diverse customer needs and preferences. Stores with narrow doorways, steep stairs, or inadequate seating options exclude segments of the population, thereby limiting their market reach and potentially inviting legal repercussions. Moreover, failing to accommodate different shoppingpreferences, such as online ordering with in-store pickup or curbside delivery, can deter tech-savvy customers and lead to missed opportunities for sales.Another critical flaw in store design pertains to lighting and ambiance. Inadequate lighting not only affects the visibility of products but also creates a gloomy atmosphere that dampens the mood of shoppers. Similarly, excessive noise levels or disruptive background music can detract from the shopping experience, making it difficult for customers to focus or engage with products. Moreover, temperature control is often overlooked, leading to uncomfortable conditions that drive customers away rather than encouraging them to linger and explore.Furthermore, the lack of flexibility in store design represents a significant flaw, especially in the context of evolving consumer preferences and market trends. Storesthat are rigid in their layout and fixtures struggle to adapt to changing demands or seasonal variations. For instance, a store with fixed shelving units may find it challenging to accommodate new product lines or promotionaldisplays effectively. Lack of flexibility also limits opportunities for experimentation and innovation in retail strategies, hindering the store's ability to stay relevant and competitive.In conclusion, while store design plays a crucial role in shaping the retail experience, it is essential to acknowledge and address the inherent flaws that may undermine its effectiveness. By prioritizing factors such as spatial planning, aesthetics, accessibility, ambiance, and flexibility, retailers can create environments that resonate with customers and drive business success. Recognizing and rectifying these flaws requires a holistic approach that considers both functional and emotional aspects of the shopping journey, ultimately fostering a more satisfying and memorable experience for customers.。
yig金属异质结构中自旋泵浦效应的研究
YIG/金属异质结构中自旋泵浦效应的研究摘要自旋流是材料内部自旋角动量的定向输运。
它既是自旋电子学中新物理效应出现的核心自由度，又是构建新一代高密度、高速度、低能耗磁性存储与处理器件中实现局域自旋（或磁矩）翻转的核心载体。
掌握自旋流的物理特性以及自旋流与材料相互作用的微观机制，已成为理解自旋与电荷和轨道多自由度耦合以及推动纯自旋流应用的关键科学问题。
本论文围绕以上关键科学问题，以钇铁石榴石/金属(YIG/NM)异质结构中的自旋泵浦效应为主要研究手段，开展了纯自旋流物理特征、有效自旋混合电导率(表征纯自旋流注入效率)、以及自旋霍尔角(表征自旋流与电荷流转化效率)三个方面的研究。
取得的主要创新性结论如下：1、 提出了获得纯自旋泵浦信号的方法，并建立了纯自旋流的空间对称性。
我们针对FM/NM 中可能同时存在自旋整流和自旋泵浦信号的问题，提出了利用YIG/NM 体系，实现纯自旋泵浦信号的测量。
发现磁化强度在xy 、yz 、xz 平面转动时，自旋泵浦和自旋整流信号的角度依赖关系明显不同。
同时，还发现了满足3cos θ角度关系的非均匀自旋泵浦信号。
因此，自旋泵浦信号的准确测量需要利用空间对称性排除自旋整流影响，在=90θ 或Hall 端进行测量。
2、 实现了1Pt Pd x x −(01x ≤≤)合金自旋霍尔角的准确表征，并提出了1Pt Pd x x −合金自旋霍尔角的主要微观机制。
通过标定自旋扩散长度、有效混合电导率、以及微波磁场大小，利用=90θ 几何下测量的YIG/1Pt Pd x x −自旋泵浦信号，确定了1Pt Pd x x −合金的自旋霍尔角(Pt =0.1250.015SH θ±)。
利用自旋霍尔角与电荷电导率的标度关系，通过自旋霍尔角随x 的变化，揭示了斜散射是1Pt Pd x x −中自旋相关散射的主要微观机制。
3、 提出了有效自旋混合电导率与磁化强度进动的关系，实现了有效混合电导率的调控。
Infrared absorption from Charge Density Waves in magnetic manganites
a r X i v :co n d -m a t /9810121v 1 [c o n d -m a t .s t r -e l ] 9 O c t 1998Infrared absorption from Charge Density Waves in magnetic manganitesP.Calvani,G.De Marzi,P.Dore,S.Lupi,P.Maselli,F.D’Amore,and S.GagliardiIstituto Nazionale di Fisica della Materiaand Dipartimento di Fisica,Universit`a di Roma “La Sapienza”,Piazzale A.Moro 2,I-00185Roma,ItalyS-W.CheongAT&T Bell Laboratories,Murray Hill,New Jersey 07974,U.S.A.and Department of Physics,Rutgers University,Piscataway,New Jersey 08855,U.S.A.(February 1,2008)The infrared absorption of charge density waves coupled to a magnetic background is first ob-served in two manganites La 1−x Ca x MnO 3with x =0.5and x =0.67.In both cases a BCS-like gap 2∆(T ),which for x =0.5follows the hysteretic ferro-antiferromagnetic transition,fully opens at a finite T 0<T Neel ,with 2∆(T 0)/k B T c ≃5.These results may also explain the unusual coexistence of charge ordering and ferromagnetism in La 0.5Ca 0.5MnO 3.PACS numbers:,78.20.Ls,78.30.-jThe close interplay between transport properties and magnetic ordering in the colossal magnetoresistance (CMR)manganites La(Nd)1−x Ca(Sr)x MnO 3is presently explained in terms of magnetic double exchange pro-moted by polaronic carriers along the path Mn +3-O −2-Mn +4.[1]Charge hopping promotes the alignment of Mn +3and Mn +4magnetic moments,and vice versa.The polaronic effects are due to the dynamic Jahn-Teller dis-tortion of the oxygen octahedra around the Mn +3ions.The above mechanism explains how,in manganites with 0.2<x <0.48,any increase in the magnetization en-hances the dc conductivity,and vice versa.However,La 0.5Ca 0.5MnO 3shows an unpredicted coexistence of fer-romagnetism and incommensurate charge ordering (CO).This compound is paramagnetic at room temperature,becomes ferromagnetic (FM)at T c ≃225K and,by fur-ther cooling (C),antiferromagnetic (AFM)at a N´e el tem-perature T C N ≃155K.[2]Upon heating the sample (H)the FM-AFM transition is instead observed at T HN ≃190K .[3]The dc conductivity σ(0)of La 0.5Ca 0.5MnO 3is quite insensitive to the PM-FM transition at T c .[3]X-ray,neutron [4]and electron diffraction [5]show quasi-commensurate charge and orbital ordering in the AFM phase with wavevector q =(2π/a )(13,where the charge ordering is commen-surate with the lattice.Below T CO ,the system enters at T N an antiferromagnetic phase.For x =0.67,T N ≃140K.In the present paper,the unexpected coexistence of incommensurate charge ordering and ferromagnetism in La 0.5Ca 0.5MnO 3is investigated by infrared spec-troscopy.The spectra of stoichiometric LaMnO 3andof La 0.33Ca 0.67MnO 3are also examined for comparison.Both doped manganites allow to study the optical re-sponse of charge density waves (CDW)interacting with a magnetic background.Such an experiment could hardly be done in the low-dimensional systems where CDW are usually observed.The present infrared spectra have been collected on the same La 1−x Ca x MnO 3samples,prepared as described in Ref.[3],where the above diffraction studies [5,6]have been performed.The oxygen stoichiometry has been accurately controlled,[5]to fulfill doping requirements which are particularly strict at x =0.5.The sinther-ized compound has been finely milled,diluted in CsI (1:100in weight),and pressed into pellets under vac-uum.One thus obtains reliable data when both the re-flectance and the transmittance of the sample are too low,as shown in similar experiments [7]on La 2−x Sr x NiO 4and Sr 2−x La x MnO 4.The infrared intensity I s transmitted by the pellet containing the oxide and that,I CsI ,transmit-ted by a pure CsI pellet,have been measured at the same T .One thus obtains a normalized optical density that,as shown in Ref.[8],is proportional to the optical con-ductivity σ(ω)of the pure perovskite,over the frequency range of interest here:O d (ω)=ln [I CsI (ω)/I s (ω)]∝σ(ω)(1)The spectra have been collected by two interferometers between 130and 10000cm −1,and by accurately ther-moregulating the samples within ±2K between 300and 20K.The susceptibility χ(T )of La 0.5Ca 0.5MnO 3has been measured at zero static field in a commercial ap-paratus by the Hartshorn method,at a frequency of 127Hz.The optical density O d (ω)of La 0.5Ca 0.5MnO 3is com-pared in Fig.1with that of stoichiometric LaMnO 3.The latter compound shows in Fig.1(a)a negligible absorp-tion in the midinfrared at all temperatures.At least 101phonon lines,out of the 19predicted[9]under theor-thorombicsymmetry of LaMnO 3,are also found out in Fig.1(a)by a fit to Lorentians.A detailed analysis of the phonon spectrum of this family of manganites will be reported elsewhere.ω ( cm -1)O p t i c a l d e n s i t yFIG.1.The optical density O d of polycrystalline LaMnO 3(a)and La 0.5Ca 0.5MnO 3(b)as the sample is cooled from 300K to 20K.The dashed lines in (b)represent extrapolations based on Eq.(3).Let us now consider Fig.1(b),where the optical den-sity of La 0.5Ca 0.5MnO 3is reported for decreasing tem-peratures.At 300K the phonon peaks are shielded by abroad background which,after a straightforward compar-ison with Fig.1(a),can be attributed to the mobile [10]holes introduced by Ca doping.However,at a T between 245and 215K,a minimum appears in that background,which gradually deepens by further lowering the temper-ature.This signature of an optical gap provides evidence for increasing localisation of the carriers.Indeed,as T lowers,phonon peaks similar to those in Fig.1(a)become more and more evident,showing that the screening action of the mobile holes weakens.Moreover,the states lost in the gap region for decreasing temperature are transfered to higher frequencies (see the crossing point of the ab-sorption curves at ≃1500cm −1),not to a coherent peak at ω=0.This finding is consistent with the regular de-crease in σ(0)[3]observed in La 0.5Ca 0.5MnO 3betweenroom temperature and T N .A loss of spectral weight such as in Fig.1(b)can be measured by the variation of an effective number of car-riers n eff (T ),obtained by integrating σ(ω)between two suitable frequencies.By taking into account Eq.(1),we can define for the present purpose a quantity:n ∗eff (T )=ω2ω1O d (ω)dω∝n eff (T )(2)As suitable integration limits one may take the two fre-quencies where O d (ω)does not appreciably change with temperature,ω1=200cm −1and ω2=1500cm −1.The values thus obtained for n ∗eff (T )along a thermal cycle are plotted in Fig.2(a).The inset compares the spectra observed at the same T =160K upon cooling and heating the sample.When the latter is cooled from T >∼T c ,spec-tral weight is increasingly lost in the far infrared.A com-parison with the corresponding curves of the magnetic susceptibility χ(T )in Fig.2(b)shows that the decrease in n ∗eff (T )is completed well below the N´e el temperature T C N .Full localisation of the carriers is then observed only when χ(T )has reached its minimum value and an AFM phase is established in the whole sample.When heat-ing the sample,n ∗eff (T )starts increasing around 120K,again well below T HN .The behavior of the infrared absorption in Fig.1(b)and 2(a)in a temperature range where electron diffrac-tion observes incommensurate charge ordering,points to-ward the formation a charge density wave.One can then extract from Fig.1(b)the optical gap 2∆(T )and com-pare its behavior with that expected for a CDW.In that case,σ(ω)at ω>∼2∆(T )is similar to that of a semicon-ductor in the presence of direct band to band transitions.[11]By remembering again Eq.(1),one can then fit to the experimental O d (ω),for ω>∼2∆(T ),the expression:σ(ω)∝[ω−2∆(T ))]α.(3)The curves thus obtained,reported as dashed lines in Fig.1(b),well describe the resolved part of the gap profile at all temperatures with the same α=1∆0T(4)2χ ( 10-3 e m u / g )n *e f f ( c m -1 )2∆ ( c m -1 )Temperature ( K )FIG.2.Effective number of carriers n ∗ef f (T )(a),zero-field magnetic susceptibility χ(T )(b),and width of the optical gap 2∆(c)vs.temperature in La 0.5Ca 0.5MnO 3,as the sample is cooled (full circles,solid lines)or heated (open circles,dashed lines).The lines in (a)are guides to the eye,those in (c)are fits to Eq.(5).The inset in (a)shows the optical densities measured at the same T =160K by cooling (solid)and heat-ing (dashed).In (b),the T C N and T HN values here found at a static field H =0are slightly higher than reported in Ref.[3]for H =1T.In (c),the star corresponds to the activation energy extracted from the dc resistivity of Ref.[3](see text).Unlike for an ordinary CDW,here the antiferromagnetic background fully localizes the charges at a finite T 0<T N ,which moreover depends on the thermal procedure.We find that this effects can be simply taken into account byreplacing in Eq.(4)T =0by T X0(X =C,H ):∆(T )/∆0=tanh∆(T )(T c −T X0)the Mn 3d and O 2p orbitals.In La 0.5Ca 0.5MnO 3,the hopping of polaronic carriers would then be able to estab-lish a double-exchange mechanism,not effective enough to establish ferromagnetism and high dc conductivity in the whole sample.The above phase-separation scenario for La 0.5Ca 0.5MnO 3at T c >T >T N is consistent with the present spectra at infrared wavelengths,where any inhomogeneity on a scale much larger than L is averaged out.In Fig.1(b),the (poorly)mobile holes of the FM regions then appear as they were the excited states of the commensurate CDW condensate in the AFM clus-ters.The consistent behaviors of χ(T ),n eff (T),and ǫ(T )between T c and T 0are easily explained:all those quantities in fact measure in different ways the increas-ing size of the AFM clusters at the expense of the FM regions.2∆ ( c m -1 )Temperature ( K )FIG. 3.Width of the optical gap 2∆(T )in La 0.33Ca 0.67MnO 3,with its fit to Eq.(5)(solid line).The spectra used to extract 2∆(T )by the extrapolations based on Eq.(3)(dashed lines)are shown in the inset.However,in order to firmly establish the above inter-pretation,it remains to show that the regions with com-mensurate CO may produce an infrared gap which be-haves according to Eq.(5).To this purpose,we show in Fig.3the midinfrared spectra of La 0.33Ca 0.67MnO 3.This sample exhibits commensurate charge ordering be-low T CO =265K,with wavevector q =(2π/a )(1[1]lis et al.,Phys.Rev.Lett.74,5144(1995),andreferences therein.[2]P.G.Radaelli et al.,Phys.Rev.Lett.75,4448(1995).[3]P.Schiffer et al.,Phys.Rev.Lett.75,3336(1996).[4]P.G.Radaelli et al.,Phys.Rev.B 55,3015(1997).[5]C.H.Chen and S-W.Cheong,Phys.Rev.Lett.76,4042(1996).[6]A.P.Ramirez et al.,Phys.Rev.Lett.76,3188(1996).[7]P.Calvani et al.,Phys.Rev.B 54,R9592(1996).[8]A.Paolone et al.,Physica B 244,33(1998).[9]M.Couzi and P.Van Huong,J.Chim.Phys.(France)69,1339(1972).[10]The non vanishing dc conductivity of La 0.5Ca 0.5MnO 3at300K (σ(0)=100Ω−1cm −1)[3])does not contradict the absorption drop observed in Fig.1(b)for ω<250cm −1.The latter effect is due to the penetration depthλ∝1/√。
空间顺序构成与年代顺序作用 Spatial order and chronology英语作文
空间顺序构成以及年代作用Spatial order composition and the role of chronology in apiece of writingSpatial order refers to the method of organization in the writing work. In spatial order, details are explained as per their physical location. A writer has to arrange the ideas of the content or story so that it can create a visual sequence in the reader’s mind.While writing the essay, story or any narration, we often put emphasis on things like content quality, grammar, usage of vocabulary, length of the sentence, etc. But we tend to ignore the significance of spatial order. But, it is of vitalimportance for the whole plot. If you are describing a scenario in a story, you need to describe all the elements as per their specific order. In this way, it becomes easy for readers to understand the scene. Thus, you can see how spatial order has a significant role in most of the writing work.Spatial order helps in organizing the content, All the details are according to the order of their location in space. The usual order is from left to right and top to bottom. The readers get good help in comprehending the story.Today through this article, I would like to throw some light on different aspects of Spatial order.You will read the following things in this article:How to write a spatial order essay?What is a chronology in literature and writingDifferent types of chronologyThings to remember while writing a spatial order essayWhat are spatial order signal words?If you are looking forward to writing an impressive high school essay or college academic paper, you need to work specifically on the logical organization of the content. For this, you have to work on your thought process. You have to work on your ideas that are booming in your mind. For instance, while writing a story, thousands of thoughts can come in your mind. Some could be absurd or never follow any order. Therefore, youneed to write down all the thoughts on paper first. Once you have all ideas and thoughts in front of you, work on organization. To create an appealing and awestruck story, you need to arrange all scenes in a sequence first. By doing this, you will help the readers to get a proper understanding of the scene.Thus, spatial order is used mostly in descriptive writing. The purpose of using spatial order or organizing the information as per the location in spaces is to convey the exact scene as it was observed when appeared.How to write a spatial order essay?Uses of spatial order are not limited to storytelling only. It is also used in writing anessay as well. Here I am going to write about how beginners can work on spatial order essays.Brainstorming for ideasThe first thing to do is brainstorming. You must ask a few questions from yourself. What do you want to write? What is the purpose of writing this? Questions can also be related to the description as well. For example, you have to describe a garden, talk about the position of the bench in the garden, the number of trees, describe the colours you are seeing.Use referencesOther types of references you can take from any magazines, photos, or scenery. References help in guiding you. They will keep you on the righttrack and you will get various things to write upon.Outlining the essayAn outline will bring flow in the essay. While creating the outline be specific which location you want to keep for the essay. If you are describing an event from past to present, keep it that way. Digressions will lead to confusion and loss of spatial order.Write your essayOnce you are done with the outline, start writing the essay. Never use a vocabulary that is tough for you. Keep things simple initially. After completing the writing work, read your essay and edit if required.What is a chronology in literature and writing?The word chronology signifies arrangement. It is the arrangement of various events as per their timeline. In literature, most of the writers prefer to describe the stories in the form of a sequence of events. They unfold the events in the order in which they occurred in time. This arrangement is termed as chronological order. The audience finds such stories easy to understand. But there are authors who never follow chronology. They start the story from the end and describe in a backward manner.One can define chronology as, a science of ordering events as per the timeline. Chronology is important in all the disciplines. For example, if you are studying mathematics, the teacher starts with the basics then move to complicated topics.Therefore, following a chronological order is necessary for almost all fields.An example that will help you to understand CHRONOLOGYOften writers use the timeline to express the chronology. Here I am providing you with an example that will let you understand how you can make use of chronology in a piece of writing.Today I woke up at 7 o’clock and went jogging. I returned home at 8 am and had breakfast. After that, I left for my workplace around 9 o’clock. There, I had a meeting with the manager to discuss the work. We both had coffee together at 3 pm. I returned to my place at around 5 pm.Though it is a small example just to let you all know how to write things chronologically. There are many examples one can find in literature where writers have used this technique for story writing.Different types of chronologyChronology is easy to understand as it is completely based on time. But most of the authors use three types of chronology mainly,Linear chronology: In this type of chronology a writer tells the story in sequential order. The events are as per the timeline.Reverse chronology: Here the time sequence gets reverse. The writer starts from the ending,shares various events and ends the plot at the beginning.Nonlinear chronology: This type of chronology does not follow any specific order. Here the events are not in line. There are lots of digression in nonlinear chronology.Things to remember while writing a spatial order essayNow you have understood two important terms, one is spatial order and the other one is chronology. Now it is time to know how to write a paragraph in spatial order.Choose an appealing topicSpatial order is linked to the physical location of the subject matter, therefore, you have to be careful while selecting the topic. It should convey the meaning of the essay. While you are beginning to write spatial order essay, first think about the scene you want to write. Secondly, think from the reader’s perspective and make a list of things that you want to describe. You have to set on the things you want to describe and how such things relate to the whole story.Arrangement of informationNow you have a set of things and elements you want to put in your essay. Decide the logical order for them. Choose a starting point and an ending point as well. For instance, if you have started to describe something on left then movetowards the right. Similarly, you can use the top to bottom order as well.Use of transition wordsOne of the most important things students should keep in mind is the usage of transition words. Transition words play a significant role in creating relationships in the provided details. Therefore, students should use a certain amount of it in the spatial order writing work. Examples of transition words are, however, nevertheless, moreover, similarly, also, in the same way, likewise, although, furthermore, in spite of, in contrast, at the same time, while this might be true, on one hand, for example, for instance, in fact, indeed, of course, specifically, that is, to illustrate, etc.If you are still not clear how to write a spatial order essay, then learn the craft of essay writing from the experts.What are spatial order signal words?Spatial order signal words are prepositions. They are used to notify the location, place and position of the subject. These words are used by a writer when he or she describes the spatial organization in an essay. Often such phrases or words are applied at the beginning of the sentences. This helps in creating affinity between ideas and sentences used. Signalling words helps in the formation of a real picture in the mind of the readers. Such words make the understanding of the whole text easy. Here I am providing a list of signalling words used in spatial order.IntoAcrossNext toAboveThroughBesideOppositeAgainstBetweenOn the left handOn the right handBelowBeneathAttached toNearbyAt the top ofTo the side ofBehindIn front ofAlongsideIf you are planning to write a spatial order essay, never miss using these words.。
Electro-dynamics
D = ε 0E + P
B: magnetic induction H: magnetic field
H=
B
µ0
−M
magnetization
MIT 2.71/2.710 10/06/04 wk5-b-14
µ 0ε 0 ≡
1 c
2 vacuum
cvacuum: speed of light in vacuum
ε = (1 + χ )ε 0 ≡ n 2ε 0
n: index of refraction
µ 0ε =
p = q+ r+ − q−r−
Dipole moment
Polarization
P = ∑p
± ± ±
–+ –+ –+
–+ –+ –+
–+ –+ –+
– + – + – +
Spatially variant polarization induces local charge imbalances (bound charges)
MIT 2.71/2.710 10/06/04 wk5-b-3
dF
II ′ = µ0 dl 2πr
(magnetic) permeability of free space
Note the units…
⎛ Electric ⎞ 1 ⎛ Charge ⎞ ⎜ ⎟ ⎜ force ⎟ = ε ⎜ Distance ⎟ ⎠ ⎠ ⎝ 0 ⎝ ⎛ Magnetic ⎞ ⎛ Charge ⎞ ⎜ ⎟ ⎜ force ⎟ = µ 0 ⎜ Time ⎟ ⎝ ⎠ ⎠ ⎝
Charge Relaxation and Dephasing in Coulomb Coupled Conductors
a r X i v :c o n d -m a t /9902320v 1 [c o n d -m a t .m e s -h a l l ] 24 F eb 1999CHARGE RELAXATION AND DEPHASING IN COULOMB COUPLEDCONDUCTORSMarkus B¨u ttiker and Andrew M.MartinD´e partement de Physique Th´e orique,Universit´e de Gen`e ve,CH-1211Gen`e ve 4,Switzerland(February 1,2008)The dephasing time in coupled mesoscopic conductors is caused by the fluctuations of the dipo-lar charge permitted by the long range Coulomb interaction.We relate the phase breaking time to elementary transport coefficients which describe the dynamics of this dipole:the capacitance,an equilibrium charge relaxation resistance and in the presence of transport through one of the con-ductors a non-equilibrium charge relaxation resistance.The discussion is illustrated for a quantum point contact in a high magnetic field in proximity to a quantum dot.Pacs numbers:72.70.+m,72.10.-d,73.23.-bMesoscopic systems coupled only via the long range Coulomb forces are of importance since one of the sys-tems can be used to perform measurements on the other [1].Despite the absence of carrier transfer between the two conductors their proximity affects the dephas-ing rate.Of particular interest are which path detectors which can provide information on the paths of a car-rier in an interference experiment [2–4].It is understood that at very low temperatures the basic processes which limit the time τφover which a carrier preserves its quan-tum mechanical phase are electron-electron interaction processes [5,6].For the zero-dimensional conductors of interest here,the basic process is a charge accumulation in one of the conductors accompanied by a charge de-pletion in the other conductor.The Coulomb coupling of two conductors manifests itself in the formation of a charge dipole and the fluctuations of this dipole governs the dephasing process.The dynamics of this dipole,and thus the dephasing rate,can be characterized by elemen-tary transport coefficients:In the absence of an external bias excess charge relaxes toward its equilibrium value with an RC -time.In mesoscopic conductors [7]the RC -time is determined by an electrochemical capacitance C µand a charge relaxation resistance R q .In the presence of transport through one of the conductors,the charge pile-up associated with shot noise [8],leads to a non-equilibrium charge relaxation resistance [9]R v .Below we relate R q and R v to the dephasing rate.Renewed interest in dephasing was also generated by experiments on metallic diffusive conductors and a sug-gested role of zero-point fluctuations [10].We refer to the resulting discussion only with a recent item [11].More closely related to our work are experiments by Huibers et al.[12]in which the dephasing rate in chaotic cavi-ties is measured.At low frequencies such cavities can be treated as zero dimensional systems [13].Consider two mesoscopic conductors coupled by long range Coulomb interactions.An example of such a sys-FIG.1.Quantum point contact coupled to a quantum dot either in position A or B.tem,suggested in Ref.[14],is shown in Fig. 1.In case A,a quantum point contact (QPC)in a high magnetic field is close to a quantum dot and in case B the QPC is some distance away from a quantum dot.First we fo-cus on case A.To describe the charge dynamics of such a system we use two basic elements.First we character-ize the long range Coulomb interaction with the help of a geometrical capacitance,much as in the literature on the Coulomb blockade.Second the electron dynamics in each conductor (i )is described with the help of its scat-tering matrix,s (i )αβ(E,U i )which relates the amplitudes of incoming currents at contact βto the amplitudes of the outgoing currents at α.The scattering matrix is a function of the energy of the carriers and is a function of the electrostatic potential U i inside conductor i .In case A,the total excess charge on the conductor is of impor-tance.In this case the charge dynamics of the mesoscopic conductor can be described with the help of a density of states matrixN (i )δγ=1dE.(1)Eq.(1)is valid in the WKB limit in which derivatives with regard to the potential can be replaced by an energyderivative.Eq.(1)are elements of theWigner-Smithdelay-time matrix[15,16].Later,we consider also situa-tions in which energy derivatives are not sufficient.The diagonal elements of this matrix determine the densityof states of the conductor N i = γTr(N (i )γγ);the trace is over all quantum channels.The non-diagonal elements are essential to describe fluctuations.At equilibrium,if all contacts of conductor i are held at the same potential,the two conductors can be viewed,as the plates of a capacitor holding a dipolar charge dis-tribution with an electrochemical capacitance [7]C −1µ=C −1+D −11+D −12which is the series combination of the geometrical capacitance C of the two conductors,and the quantum capacitances D i =e 2N i determined by their density of states.An excess charge relaxes with a resis-tance determined by [7]R (i )q =h[ γTr(N (i )γγ)]2.(2)In the presence of transport through the conductor i the role of the equilibrium charge relaxation resistance,Eq.(2),is played by the non-equilibrium resistance [9]R (i )v ,R (i )v=h[ γTr(N (i )γγ)]2.(3)Note that the charge relaxation resistance R (i )q invokesall elements of the density of states matrix with equal weight,but in the presence of transport the non-diagonal elements are singled out.Next we relate these resis-tances to the voltage fluctuations in the two coupled mesoscopic conductors and subsequently to the dephas-ing time.Here we mention only that at equilibrium,if all contacts at each conductor are at the same potential,the dynamic conductance of our capacitor is given byG (ω)=−iωC µ+C 2µR q ω2+O (ω3).Thus R q determines the dissipation associated with charge relaxation on the two conductors.Charge and potential fluctuations are related byˆQ=C (ˆU 1−ˆU 2)=e ˆN 1−e 2N 1ˆU 1.(4)−ˆQ=C (ˆU 2−ˆU 1)=e ˆN 2−e 2N 2ˆU 2.(5)ˆQis the charge operator of the dipole.These equations state that the dipole charge Q on conductors 1and 2can be written in two ways:First it can be given by the po-tential differences and the geometrical capacitances and second it can be expressed as sum of the bare charges e N 1,e N 2calculated in the absence of screening and a screening charge which here is taken to be proportional to the density of states of the conductor N i times the induced potential U i .Using D i =e 2N i for the density ofstates we find that the effective interaction G ij betweenthe two systems isG =C µC)2(C +D 2D 1)2R (2)qkT (9)with R (i )q determined by Eq.(2).Similar results hold for S U 2U 2and the correlation spectrum S U 1U 2.If a bias eV is applied,for instance to the conductor 2,we find thesame spectrum as above,except that R (2)q kT is replaced,to first order in e |V |,by R (2)v e |V |for e |V |>kT .To relate the voltage fluctuation spectra to the dephas-ing rate we follow Levinson [4].A carrier in conductor 1moves in the fluctuating potential U 1.As a consequence the phase of the carrier is not sharp but on the averagede-termined by exp(i (ˆφ(t )−ˆφ(0)) = ˆT exp(i t 0dt ′ˆU 1(t ′)) .Assuming that the fluctuations are Gaussian this quan-tum mechanical average is given by exp(−t/τφ)with τ−1φ=(e 2/2¯h 2)S U 1U 1.Since the voltage fluctuation spectrum Eq.(9)consists of two additive terms we can decompose the dephasing rate into two contributions (1/τφ)(11)and (1/τφ)(12)where the index pair (ik )indi-cates that we deal with the dephasing rate in conductor i generated by the presence of conductor k .Before discussing the results it is useful to clarify the limit in which we are interested.Typically,the Coulomb charging energy U =e 2/2C is large compared to the level spacing ∆in the conductors of interest.Since ∆i =1/N i this has the consequence that any deviations of the electrochemical capacitance from its geometrical value are very small.We can thus take C µ=C and C +D 2/D 2≈1in Eq.(9).Now we are interested in thedephasing time τ(12)φin conductor 1due to the presence of conductor 2.Our discussion gives for this contribution1¯h2Cτφ (12)=e2D1 2R(2)v e|V|,(11)with R v given by Eq.(3)if it is in a transport state with e|V|>kT.Note that for closed2D-conductors e−e-scattering leads to a rate[6]proportional to T2wheras for open conductors Eq.(10)predicts a rate which is linear in T.We now specify that transport in the conductor1is via a single resonant tunneling state.Thus the relevant density of states in conductor1is a Breit-Wigner expres-sion.For simplicity we assume that we are at resonance and hence N1=(2/πΓ),whereΓis the half-width of the resonance.The conductor2is a QPC.The resistance R q and R v for a QPC in the absence of a magneticfield have been discussed in Ref.[9].R(2)q is,R(2)q=h[ n(dφn/dE)]2(12)whereφn is the phase accumulated by carriers in then-th eigen channel of the QPC traversing the region inwhich the potential is not screened.Note that if onlya single channel is open,R(2)q is universal and given byR(2)q=he2n1dE 2VΩ VΩd3r∂where U2characterizes the potential of the edge state in ΩB.We assume that only the charge pile up in the region ΩB matters and consequently all additional phases in the scattering problem are here without relevance.The total scattering matrix of the QPC and the traversal of region ΩB is then simply s11=r,s21=t,s12=t exp(iφ2)and s22=r exp(iφ2).Consider next the charge operator.We have to evalu-ate the variation of the scattering matrix with respect to the potential U2.Only s12and s22depend on this poten-tial.Wefind ds12/edU2=(ds12/dφ2)(dφ2/edU2).But (dφ2/edU2)=−2πdN2/dE,where now dN2/dE is the density of states of the edge state in regionΩB of con-ductor2.Simple algebra now gives N(2)11=T dN2/dE,N(2)12=N(2)∗21=r∗t exp(−iφ2)dN2/dE,(15)and N(2)22=R dN2/dE.At equilibrium wefind R(2)q=h/2e2as is typical for an edgestate that is perfectly con-nected to a reservoir[17].The non-equilibrium resistance isR(2)v=(h/e2)T R.(16)Note that in the one-channel case both R q and R v are independent of the density of states N2.The addi-tional dephasing rate generated by the edge at equilib-rium in the quantum dot at resonance is(1/τφ)(12)= (π4Γ2/2hU2)kT.Note that this rate depends on the edge state only through its geometrical capacitance.In the non-equilibrium case,the additional dephasing rate caused by the chargefluctuations on the edge state is (1/τφ)(12)=(π4Γ2/hU2)T R e|V|.A rate proportional to T R is also obtained by Buks et al.[14].Of interest is the effect of screening:While in the one channel case, the rate depends on the capacitance of the edge channel only,such a universal result does not apply as soon as additional edge states are present.Thus consider an ad-ditional edge state which is transmitted with probability 1.It generates no additional noise and leaves the dc-shot noise invariant[8].But the additional edge channel con-tributes to screening.If we take the two edge channels to be close together in the regionΩB both edge channels will see the same potential U2.Now the total density of states of the two edge channels in regionΩB has a con-tribution from both the perfectly transmitted edge state (1)and edge state(2)N2=N21+N22.As a consequence the dephasing rate is now reduced and given by1hU2 N22[1]M.Field,et al.Phys.Rev.Lett.70,1311(1993).[2]E.Buks,et al.Nature391,871(1998).[3]I.L.Aleiner,N.S.Wingreen,and Y.Meir,Phys.Rev.Lett.79,3740(1997).[4]Y.Levinson,Europhys.Lett.39,299(1997).[5]B.L.Altshuler,A.G.Aronov and D.Khmelnitskii,J.Phys.C15,7367(1982).[6]U.Sivan,I.Imry and A.G.Aronov,Europhys.Lett.28,115(1994);Y.M.Blanter,Phys.Rev.B54,12807(1996).[7]M.B¨u ttiker,H.Thomas,and A.Pretre,Phys.Lett.A180,364,(1993).[8]M.B¨u ttiker,Phys.Rev.Lett.65,2901(1990);Phys.Rev.B41,7906(1990).[9]M.H.Pedersen,S.A.van Langen and M.B¨u ttiker,Phys.Rev.B57,1838(1998).[10]P.Mohanty,E.M.Q.Jariwalla and R.A.Webb,Phys.Rev.Lett.79,3306(1997).[11]A.Zawadowski,Jan von Delft, D. C.Ralph,cond-mat/9902176[12]A.G.Huibers,et al.Phys.Rev.Lett.81,200(1998).[13]P.W.Brouwer and M.B¨u ttiker,Europhys.Lett.37,441-446(1997).[14]E.Buks,D.Sprinzak,M.Heiblum,D.Mahalu,V.Uman-sky and H.Shtrikman,(unpublished).[15]F.T.Smith,Phys.Rev.118349(1960).[16]Y.V.Fyodorov and H.J.Sommers,Phys.Rev.Lett.76,4709(1996);V.A.Gopar,P.A.Mello,and M.B¨u ttiker, Phys.Rev.Lett.77,3005(1996);P.W.Brouwer,K.M.Frahm,and C.W.J.Beenakker,Phys.Rev.Lett.78, 4737(1997);C.Texier and tet,cond-mat/981219.[17]M.B¨u ttiker and T.Christen,in’High Magnetic Fields inthe Physics of Semiconductors’,edited by ndwehr and W.Ossau,(World Scientific,Singapur,1997).p.193.cond-mat/9607051。
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a r X i v :c o n d -m a t /0405350v 1 [c o n d -m a t .m e s -h a l l ] 16 M a y 2004Spatial ordering of charge and spin in quasi one-dimensional Wigner moleculesB.Szafran,1,2F.M.Peeters,1S.Bednarek,2T.Chwiej,1,2and J.Adamowski 21Departement Natuurkunde,Universiteit Antwerpen (Campus Drie Eiken),B-2610Antwerpen,Belgium2Faculty of Physics and Nuclear Techniques,AGH University of Science and Technology,al.Mickiewicza 30,30-059Krak´o w,Poland Few-electron systems confined in quasi one-dimensional quantum dots are studied by the config-uration interaction approach.We consider the parity symmetry of states forming Wigner moleculesin large quantum dots and find that for the spin-polarized Wigner molecules it strictly depends on the number of electrons.We investigate the spatial spin-ordering in the inner coordinates of the quantum system and conclude that for small dots it has a short-range character and results mainly from the Pauli exclusion principle while the Wigner crystallization in large dots is accompanied by spin ordering over the entire length of the dot.I.INTRODUCTIONStrong confinement of charge carriers in two directions results in reduction of their degrees of freedom to a sin-gle one,i.e.,in quasi one-dimensional motion.Such one-dimensional systems are realized typically in split-gate 1,2and cleaved-edge overgrowth 3semiconductor quantum wires,as well as in carbon nanotubes,4but can also be realized in finite-size systems,i.e.,in anisotropic quan-tum dots 5or quantum rings.6There is a renewed in-terest in the one-dimensional systems related to the re-cent progress of vapour-liquid-solid fabrication of quan-tum wires of very high quality.7,8,9The present paper is devoted to electron systems con-fined in one-dimensional quantum dots and in particu-lar to their Wigner crystallization 10appearing when the electron-electron interaction dominates over the kinetic energy.Wigner electron solids (Wigner molecules)are predicted to appear in large dots 11or in strong mag-netic fields.12In the Wigner molecules the charge den-sity separates into distinct charge maxima each corre-sponding to one of confined electrons.Formation of Wigner molecules in the ground-state charge density in one-dimensional quantum dots was previously obtained in exact diagonalization 13,14,15and density functional approach.16In one-dimensional dots the Wigner local-ization appears in the laboratory frame,in contrast to the inner-coordinate crystallization appearing in circu-lar quantum dots,12including quantum rings.Trans-port properties of Wigner crystals formed in open infi-nite one-dimensional systems have also been studied.17,18The Luttinger liquid formalism has been applied 19to quantum wires with box-like boundary conditions,i.e.,to the one-dimensional quantum dots.Melting of clas-sical one-dimensional Wigner crystals has recently been described.20We study the quasi one-dimensional quantum dots us-ing a configuration interaction approach with the effec-tive electron-electron interaction potential which we de-rived recently.21This work is a generalization of our ex-act two-electron study 15to larger number of electrons.In the weak confinement limit the ground-state becomes nearly degenerate with respect to the spin configurationof the electron system.14,15Similar approximate degen-eracy has been found in quantum rings of large radius.22In this paper we study the parity symmetry of the nearly degenerate states forming Wigner molecules in large dots.We show that for spin-polarized electrons the Wigner lo-calization is formed only for one (even or odd)spatial parity of the state strictly dependent on the number of electrons.We present this dependence in the form of a theorem for which we provide a rigorous analytical proof.The found dependence of the parity of one-dimensional Wigner molecule states on the number of electrons is sim-ilar to the appearance of the magic angular momenta states for which Wigner crystallization is possible in cir-cular dots.23,24Furthermore,we discuss an inhibition of Wigner crystallization by a perturbation of the confine-ment potential through a central inversion-invariant po-tential well.Magnetic spin-ordering of electrons in one-dimensional space has been extensively studied 25in Hubbard mod-els which,in one dimension with only nearest-neighbor hopping interactions,predict the appearance of a low-spin ground state.26This is a consequence 26of the Lieb-Mattis theorem 27which implies that with-out spin-dependent interactions the ground-state of one-dimensional electron systems corresponds to the lowest possible spin quantum number (S =0or 1/2).This fea-ture generally does not have to result in any spatial spin ordering.In this paper we use the exact numerical solu-tion of the Schr¨o dinger equation to investigate the spatial distribution of spins in the one-dimensional quantum dot and the relation between the charge and spatial spin or-dering in the Wigner crystallization limit.We find that Wigner crystallization is accompanied by a long-range spin-ordering in the inner coordinates of the system in-stead of a spin-symmetry breaking predicted by density functional theory.16,28In the ground-state this ordering has a clear antiferromagnetic character.This paper is organized as follows.In Section II we present the theoretical method.Section III contains the results for the Wigner localization and ground state de-generacy of the few electron systems.In Section IV we present proof for the dependence of the parity of spin-polarized Wigner molecules on the number of electrons.Section V contains discussion of the effect of a central de-fect on Wigner crystallization.In Section VI the study of spin ordering is presented.Section VII contains our summary and conclusions.II.THEORYWe consider N electrons confined in a quasi-one-dimensional quantum dot with strong lateral harmonic-oscillator confinement potential.The Hamiltonian of the system reads,H=Ni=1h i+N i=1N j>iκ2m∗∇2+m∗ω22(κ/l)×erfc z ij/21/2l exp(z2ij/2l2),(3) where z ij=|z i−z j|andh1D=−¯h2dz2+V(z)(4)is the single-electron one-dimensional Hamiltonian.In the following we will neglect thefirst term in Eq.(3), i.e.,the lateral confinement energy which is indepen-dent of the form of wave functions in the z direction. The last term in Eq.(3)is the effective interaction energy21for electrons in a quasi-one-dimensional envi-ronment resulting from integration of the Coulomb po-tential over the lateral coordinates,m∗is the effective mass,κ=e2/4πε0ε,εis the dielectric constant,and l=-30-20-100102030z [nm]c h a r g e d e n s i t y [a r b . u n i t s ]d=50 nm0+1+1-(b)0--60-40-200204060z [nm]c h a r g ede n s i t y [a r b . u n i t s ](c)0+1-1+d=100 nm0--100-50050100z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=200 nm (d)0+1-0- 1+4080120160200d [nm]0.40.81.21.62.0E x d [e V x n m ]0+1-0-1+(a)FIG.1:(a)Lowest energy levels multiplied by the dot length for N =2.Numbers close to the curves denote the total spinquantum number of the corresponding states and signs +,−stand for even and odd parity symmetry.(b),(c),(d)-charge density of 0+,1−,1+and 0−states plotted with solid,dotted,dashed and dash-dotted lines for d =50,100and 200nm,respectively.-30-20-100102030z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=50 nm(b)1/2-1/2+3/2--75-50-250255075z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=150 nm(c)1/2-1/2+3/2--100-50050100z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=200 nm (d)1/2- 1/2+ 3/2-3/2+4080120160200d [nm]1.01.52.02.53.03.5E x d [e V x n m ]1/2-3/2+3/2-1/2+(a)FIG.2:(a)Lowest energy levels multiplied by the dot length for N =3.(b),(c),(d)-charge density of 1/2−,1/2+and 3/2−states plotted with solid,dashed and dotted lines for d =50,150and 200nm,respectively.In (d)the charge density of the 3/2+state is shown by the dash-dotted curve.separation of electron charges into two charge islands,i.e.,the Wigner crystallization.Fig.1shows that the singlet-triplet degeneracy obtained previously 15for the two-electron ground-state appears also in the first excited state.Fig.2(a)shows the energy levels and Figs.2(b-d)the charge density for the lowest-energy states of the 3-electron system for increasing d .For 3electrons the Wigner molecule is formed in states 1/2−,1/2+and 3/2−which become degenerate for large d .In the state 3/2+the charge density exhibits four maxima [cf.Fig.2(d)],which apparently prevents this state to be degen-erate with the ground state.In the 4-electron system the ground state corresponds to 0+symmetry.The states 1−,1+and 2+for large dots [cf.3(a)]tend to the degeneracy with the ground state.The charge densities of these states for large dots present four distinct maxima [cf.Fig.3(d)].Energy lev-els corresponding to states 0−and 2−are separated by a significant energy distance from the ground state [cf.Fig.3(a)]and in large dots they correspond to identi-cal charge densities with five maxima.The ground state charge density evolution obtained for N=3and 4is in aqualitative agreement with the results of Ref.[13].Finally,in the 5-electron system the ground-state of 1/2+symmetry becomes degenerate with 1/2−,3/2+,3/2−,and 5/2+states [cf.Fig.4(a)]form-ing Wigner molecules for large dots [cf.Figs.4(b-d)].The spin polarized state of odd parity 5/2−does not become degenerate with the ground-state and its charge density in large dots forms six maxima [cf.Fig 4(d)].In the entire d range and for all electron numbers stud-ied the order of the lowest energy levels for given total spin quantum numbers (neglecting the parity)follow the order of the spin quantum numbers,which is in agree-ment with the theorem of Lieb and Mattis.27In large dots a ground-state degeneracy appears.In Ref.[14]the degeneracy was interpreted in terms of a vanishing tunnel coupling between the local minima of the total N -dimensional potential energy.The present results in-dicate that the nearly degenerate states possess the same charge density in the laboratory frame.Moreover,we observe the following regularities.In the limit of Wigner localization the ground state of the N -electron system appears for N different pairs of the spin and parity quan-tum numbers.29For even electron numbers N =2and 4,-50-2502550z [nm]c h a r g ede n s i t y [a r b . u n i t s ]0+d=100 nm (b)1-1+2+-100-50050100z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=200 nm (c)2+0+1+1-z [nm]c h a r g ede n s i t y [a r b . u n i t s ]50100150200250300d [nm]23456E x d [e V x n m ](a)1-1+2+2-0-0+FIG.3:(a)4-electron energy levels multiplied by the dot length.(b),(c),(d)-charge density of 0+,1−,1+and 2+4-electron states plotted with solid,dash-dotted,dotted and dashed lines for d =100,200and 300nm,respectively.In (d)the charge densities of 2−and 0+states are marked with crosses and dots,respectively.-50-2502550z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=100 nm (b)1/2+1/2-3/2+5/2+3/2--1000100z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=200 nm (c)1/2+5/2+3/2+1/2-3/2-50100150200250300d [nm]46810E x d [e V x n m ]1/2-3/2+3/2-5/2+5/2-(a)1/2+1/2--1000100z [nm]c h a r g ede n s i t y [a r b . u n i t s ]d=300 nm 5/2-(d)1/2+ 3/2-FIG.4:(a)5-electron energy levels multiplied by the dot length.Even (odd)parity levels are plotted with solid (dotted)lines.(b),(c)-charge density of 1/2+,1/2−,3/2+,3/2−and 5/2+states plotted with solid,dash-dotted,dotted,dashed and dash-double-dot lines for d =100and 200nm,respectively.In (d)the charge density of the 1/2+,3/2−and 5/2−state is shown by solid,dashed and dotted lines,respectively [charge densities of 1/2−,3/2+and 5/2+are almost identical with the 1/2+and 3/2−charge densities are therefore omitted in (d)for the sake of clarity].N charge maxima are formed only for even parity states with S =0,while the odd parity zero-spin states possess N +1charge maxima [cf.Figs.1(d)and 3(d)].The spin-polarized Wigner-localized state can only be formed for one (even or odd)ly,the parity of the spin-polarized Wigner molecule state is even for 4and 5elec-trons and odd for 2and 3electrons.The charge density of the spin-polarized state of the other parity exhibits N +1maxima,i.e.,the state does not form a Wigner molecule and as a consequence does not become degenerate with the ground state even for large dots.This conclusion will be cast into a theorem in the next section.IV.PARITY OF SPIN-POLARIZED WIGNERMOLECULE STATESHere we give an analytical proof of the theorem:for an odd number of electrons N =2M +1as well as for an even number of electrons N =2M the parity of one-dimensional spin-polarized Wigner-molecule state is even (odd)for even (odd)value of the integer MWe will present here the proof for an odd number of electrons (the proof for even N can be easily deduced from the present demonstration).For odd N one of the electrons resides near the center of the dot (point z 0=0,cf.Fig.5),and the others occupy spatially symmet-ric sites to the left and right of the dot around points which satisfy z k =−z −k for k =±1,±2,...±M .In the Wigner phase the total charge density possesses N max-ima corresponding to the separate single-electron charge densities.A single-electron charge |ψk (z )|2is localized around point z k .In the Wigner limit the overlap be-tween the single-electron charge densities vanishes (the proof is only valid when this overlap is negligible),so the total charge density can be expressed as their sum.Since the total charge density is symmetric with respect to the origin the following equality holds|ψk (−z )|2=|ψ−k (z )|2,(5)which results in the following relation for the single-electron wave functionsψk (−z )=e iφk ψ−k (z ),(6)positionc h a r g ede n s i t yz -2z -1z 0z 1z 2|ψ−2|2|ψ−1|2|ψ0|2|ψ1|2|ψ2|2FIG.5:Illustration to the proof that for N =2M +1or N =2M electrons the parity of the spin-polarized state which exhibits Wigner localization is accordant with the parity of M .where the phase φk is a real number.Relation (6)with changed sign of k readsψ−k (−z )=e iφ−k ψk (z ).(7)Phases φk and φ−k are not independent.Changing thesign of z in Eq.(7)and making use of relation (6)we arrive atψ−k (z )=e iφ−k ψk (−z )=e i (φ−k +φk )ψ−k (z ),(8)henceφk =−φ−k ,(9)up to an unimportant multiple of 2π.Considering rela-tion (6)for k =0and reminding that we arrive at the same value ψ0(0)(non-zero for odd N )approaching the origin from both positive and negative sides we arrive at φ0=0and consequently ψ0is an even parity functionψ0(−z )=ψ0(z ).(10)Since the considered state is spin-polarized the spin and spatial parts of the wave function can be separated into a productχ(z 1,σ1,...,z N ,σN )=α(σ1)α(σ2)...α(σN )××Ψ(z 1,z 2,...,z N ),(11)where αis an eigenfunction of the single-electron spin z -component operator.The spatial wave function Ψcan be written as a Slater determinant 30Ψ(z 1,z 2,...,z N )=ψ−M (z 1)ψ−M +1(z 1)...ψM −1(z 1)ψM (z 1)ψ−M (z 2)ψ−M +1(z 2)...ψM −1(z 2)ψM (z 2)...ψ−M (z N )ψ−M +1(z N )...ψM −1(z N )ψM (z N ).(12)We apply the parity operator on Ψand makeuse of properties (6)and (9)obtaining Ψ(−z 1,−z 2,...,−z N )=e −iφM ψM (z 1)e −iφM −1ψM −1(z 1)...e iφM −1ψ−M +1(z 1)e iφM ψ−M (z 1)e −iφM ψM (z 2)e −iφM −1ψM −1(z 2)...e iφM −1ψ−M +1(z 2)e iφM ψ−M (z 2)...e −iφM ψM (z N )e −iφM −1ψM −1(z N )...e iφM −1ψ−M +1(z N )e iφM ψ−M (z N ).(13)Phase factors can be extracted from each of the determinant columns,which yieldsΨ(−z 1,−z 2,...,−z N )=e −i (φM +φM −1+...+φ−M +1+φ−M )ψM (z 1)ψM −1(z 1)...ψ−M +1(z 1)ψ−M (z 1)ψM (z 2)ψM −1(z 2)...ψ−M +1(z 2)ψ−M (z 2)...ψM (z N )ψM −1(z N )...ψ−M +1(z N )ψ−M (z N ).(14)The phases in front of the determinant in Eq.(14)cancel according to property (9).Exchanging M pairs of cor-responding columns in the determinant we arrive at Eq.(12)but multiplied by (−1)M ,which proofs that the par-ity of spin-polarized one-dimensional Wigner molecule state is determined by the odd or even value of M .We have found that 2-and 4-electron zero-spin statescan form a Wigner-localized charge density only for even spatial parity.We are unable to proof in general that the zero-spin state with Wigner localization has to be of even parity for even N .But for N =2such a proof is easily given.In this case the spin and spatial parts of the wave function can be separated as followsχ0+(z 1,σ1,z 2,σ2)=[α(σ1)β(σ2)−α(σ2)β(σ1)]×6×[ψ1(z1)ψ−1(z2)+ψ−1(z1)ψ1(z2)].(15) Applying the parity operator to the spatial part of this wave function and making use of the properties of the single-electron wave functions given above wefind that this wave function is of even parity.Moreover,it fol-lows that construction of a symmetric spatial wave func-tion for odd-parity singlet(zero-spin)two-electron states (0−)requires at least three single-electron functions,for instance,the functionΨ0−(z1,z2)=ψ0(z1)ψ1(z2)+ψ1(z1)ψ0(z2)−ψ0(z1)ψ−1(z2)−ψ−1(z1)ψ0(z2),(16) is of odd parity provided that we take zero phase shifts in relation(6).Indeed,the0−state for N=2exhibits three charge maxima[see Fig.1(d)].Moreover,con-struction of a triplet antisymmetric spatial wave func-tion with even parity(1+)also requires at least three localized functions,for instanceΨ1+(z1,z2)=ψ0(z1)ψ1(z2)−ψ1(z1)ψ0(z2)+ψ0(z1)ψ−1(z2)−ψ−1(z1)ψ0(z2),(17) possess the required symmetries for zero phase shifts in relation(6).The charge density corresponding to wave functions(16)and(17)is the same provided that the overlaps between the functionsψi are negligible.Fig. 1(d)shows that the charge densities of the states0−and 1+are indeed indistinguishable.The area below the cen-tral maximum of the probability density of degenerate0-and1+states in Fig.1(d)is two times larger than the area below each of the extreme maxima,which can be interpreted by saying that one of the electrons stays in the neighborhood of the center of the system with100% probability while probabilities offinding the other one at the left or right end of the well are equal to50%.This fea-ture is in agreement with the probability amplitudes(16) and(17).Although in the wave functions(16)and(17) the electron positions are separated,this separation has a non-classical character since the charge maxima at the left and right ends of the dot correspond to sub-electron charges.Therefore we do not refer to this separation as Wigner localization.Average electron-electron distances in states described by wave functions(16)and(17)are smaller than in states0+,1−with two charge maxima, which leads to a larger value of the Coulomb interaction energy and consequently to an energy separation between pairs of degenerate states0+,1−and0−,1+presented in Fig.1(a)in the weak confinement limit.V.WIGNER CRYSTALLIZATION IN THEPRESENCE OF A DEFECT POTENTIAL The presence of defects can significantly perturb the Wigner crystallization in large systems.We consider here a thin attractive cavity just deep enough to bind one electron.The perturbed quantum dot potential is of the formV(z)=V well(z)+V defect(z),(18) where V defect(z)=−50meV for|z|<1nm and V defect(z)=0for|z|>1nm.The assumption that the defect is localized in the center of the system does not perturb the inversion invariance of the total potential.-30-20-100102030x [nm]chargedensityd=50 nm0+(b)1+1-0--50050x [nm]chargedensityd=100 nm0+(c)1+1-0--100-50050100x [nm]chargedensityd=200 nm0+(d)0- 1- 1+zz z50100150200d [nm]51015E[meV]0+1-0-1+(a)FIG.6:(a)Lowest energy levels for N=2as functions of the length of the well with a central attractive cavity[Eq.(18)]. Numbers close to the curves denote the total spin quantum number of the corresponding states and signs+,−stand for even and odd parity symmetry,respectively.(b),(c),(d) -charge density of0+,1−,1+and0−states plotted with solid,dotted,dashed and dash-dot curves for d=50,100and 200nm,respectively.Fig.6(a)shows that contrary to the unperturbed quantum well potential[cf.Fig.1(a)]the0−and1+ states become degenerate with the0+and1−states. Figs.6(b-d)show the evolution of the charge densities of the four considered states with increasing size of the system.For large well thickness[cf.Fig.1(d)]the charge densities of these states become indistinguishable.One of the electrons is trapped by the potential of the cen-tral cavity which results in the sharp central peak of the charge density.The probability tofind the other electron at the left or right side of the origin are equal.This differs essentially from the two-electron Wigner molecule charge density in the unperturbed dot[cf.Fig.1],for which the probability tofind an electron in the center of the well was negligible and for which each of the two charge max-ima could be associated with an integer electron charge. The formation of three maxima in the charge density is possible for all states[cf.Eqs(16)and(17),for0−and 1+states,similar formulas can be given for the other two].Therefore,the ground-state tends to a fourfold de-generacy in contrast to the double degeneracy for theunperturbed dot [cf.Fig.1(a)].-5050x [nm]c h a r g e d e n s i t yd=100 nm 1/2+1/2-3/2-3/2+(c)x [nm]c h a r g e d e n s i t yd=50 nm1/2+1/2-3/2-3/2+(b)zz50100150200d [nm]204060E [m e V ]1/2-3/2-1/2+3/2+(a)FIG.7:(a)Lowest energy levels for N =3as function of the length of the well with a central attractive cavity [Eq.(18)].Numbers close to the curves denote the total spin quantum number of the corresponding states and signs +,−stand for even and odd parity symmetry.(b),(c),(d)-charge density of 0+,1−,1+and 0−states plotted with solid,dotted,dashed and dash-dot curves for d =50,100and 200nm,respectively.Fig.7shows the lowest energy levels and correspond-ing charge density evolution for the 3-electron system.Contrary to the 2-electron system the central defect doesnot perturb the number of charge maxima,Wigner local-ization appears similarly as for the unperturbed dot [cf.Fig.2]for 1/2+,1/2−,and 3/2−states which become degenerate in the Wigner localization limit.State 3/2+,which according to the theorem given in Section IV can-not form a Wigner phase lies higher in energy,like for the unperturbed dot.The influence of the central attractive defect is quali-tatively different for odd and even electron number.For an odd number of electrons it simply enhances the lo-calization of the central electron,and does not influence the ground-state degeneracy.While for even N it de-stroys Wigner crystallization leading to the appearance of an extra charge maximum corresponding to sub-electron charge and allows more states to become degenerate with the ground-state.VI.SPATIAL SPIN ORDERING IN THEWIGNER LIMITIt is interesting to look whether the low-spin ground states exhibit any spatial antiferromagnetic ordering of the electron spins.For even number of electrons and ar-bitrary dot length the ground-state corresponds to zero total spin.In this case the spin-up and spin-down densi-ties are exactly equal to each other,so that spin-ordering is not visible in the laboratory frame of reference.In or-der to investigate a possible spin-ordering in the zero-spin ground states one has to look into the inner coordinates of the quantum system.We use here the spin-dependent pair correlation functions (PCFs)defined for a given state by the expectation valuesF same P CF (z a ,z b )=N i =1Nj>iδ(z a −z i )δ(z b −z j )(|α(σi )α(σj )><α(σi )α(σj )|+|β(σi )β(σj )><β(σi )β(σj )|),(19)andF oppo P CF (z a ,z b )=N i =1N j>iδ(z a −z i )δ(z b −z j )(|α(σi )β(σj )><α(σi )β(σj )|+|β(σi )α(σj )><β(σi )α(σj )|),(20)where αand βstand for spin-up and spin-down eigen-states respectively.Functions (19,20)give the probabil-ity of finding at positions z a and z b a pair of electrons with the same (19)or opposite (20)spins.The sum of functions (19)and (20)gives the spin-independent PCF.Fig.8(a)shows the PCF plots for the 4-electron ground state in a small quantum dot [cf.Fig.3(b)]with d =100nm.The position of one of the electrons is fixed near the right end of the dot [position marked bythe thin vertical line in Fig.8(a)].We see that the prob-ability of finding an electron with the same spin in the neighborhood of the fixed-position electron is zero,which is a signature of the Pauli exclusion principle.At the left side of the dot probabilities of finding an electron with the same or opposite spin as the one of the fixed position electron are nearly equal.For the total zero-spin states in relatively small dots the spin-ordering in the inner co-ordinates is of short range and results from the Pauli-100100x [nm]P C Fspinindependento p p o s . s p i ns a m es p i n(b)d=300nm N=4 (0+)-50050x [nm]P C F(a)spinindependents am e s p i no pp os . s pi nd=100nm N=4 (0+)-100100x [nm]P C Fspinindependent s a m e sp in opposite spind=300nmN=4 (1-)(c)zzzFIG.8:Pair correlation functions (PCFs)for 4electrons in state 0+(a,b)and state 1−with S z =¯h (c)for d =100(a)and 300nm (b,c).One of the electrons is fixed and its position is marked by a thin vertical line.Solid curves show the spin-independent PCF,dashed (dotted)curves show the opposite (same)spin PCF.exclusion.We only found a long-range inner-coordinate spin-ordering in the Wigner crystallization limit.Fig.8(b)shows the plot for the 4-electron ground state with d =300nm.The charge density of the system exhibits 4distinct maxima [cf.Fig.3(d)].We fix the position of one of the electrons at the rightmost density maximum [cf.the vertical line in Fig.8(b)].The probability that the electron in the adjacent maximum has the opposite spin is nearly 100%.The spin-dependent PCFs also dif-fer for the two charge maxima at the left of the origin.An electron confined at the first (second)charge maxi-mum to the left of the origin is more probable to have the same (opposite)spin as the one of the fixed electron.The ordering is of a probabilistic character,so that the anti-ferromagnetic order of spins is the most probable to be found,but the probability is not 100%.The spin-ordering in this state has a clearly antiferromagnetic character and its range covers the entire length of the dot.A similar inner-coordinate antiferromagnetic order was previously found for quantum rings.6The 100%probability of finding the opposite spin in the charge maximum adjacent to the maximum associ-ated with the fixed electron presented in Fig.8(b)is not,as one could naively expect,related to the Pauli exclu-sion.In Fig.8(c)we plotted the PCF for the 1−state,which becomes degenerate with the ground 0+state in the weak confinement limit.We see that in this state the spin of electrons confined in the two central maxima is independent of the spin of the electron at the rightmost maximum.However,in this state one may expect that the electrons at the opposite ends of the dot have the same spin,which means that also in this state a long-range spin-ordering exists,even if it is not of antiferro-magnetic origin.For odd number of electrons the difference between spin-up and spin-down densities appears in the labora-tory frame.This is qualitatively different from quantum rings,which in fact are endless structures.Fig.9(a)shows the spin densities for a relatively small dot length of d =100nm [too small for the ground-state Wigner localization to appear,cf.Fig.4(b)].The spin-up elec-trons tend to gather at the extreme left and right ends of the dot as well as in its center.The spin-down density is minimal in the center of the dot,and the overall spin density (difference of the spin-up and spin-down densi-ties)exhibits antiferromagnetic sign oscillations within the dot.These sign oscillations are due to the electron-electron interaction since in the noninteracting electron system the majority spin-up density is nowhere smaller than the spin-down density.For larger systems [d =250nm,cf.Fig.9(b)]the antiferromagnetic spin oscillations become more pronounced.However,for even larger d [cf.Fig.9(c)and (d)],for which the Wigner molecule appear in the 1/2+ground state,the typically antiferromagnetic real-space spin-ordering with the spin orientation chang-ing between the adjacent charge maxima vanishes.Let us look at the spin distribution in the inner coor-dinates of the 5-electron 1/2+ground state.Fig.10(a)shows the PCF plots for d =100nm.Electrons of the same spin as the fixed electron do not appear in its close neighborhood,but are more probable to be found at the center of the dot than electrons of opposite spin.Prob-ability of finding an electron at the opposite side of the dot is independent of its spin.The spin order in this relatively small dot (d =100nm)is clearly short-range which is similar as for the case of 4electrons in a small dot [cf.Fig.8(a)].The PCF plots for opposite spins at the left end of the dot start to differentiate for d =200nm [cf.Fig.8(b)].For d =300nm,for which Wigner lo-calization is observed [cf.Fig.4(d)],the PCF plots show a long-range antiferromagnetic spin ordering.Notice the growth of the PCF plot for the same spin direction in the closest neighborhood of the fixed-position electron from d =200to 300nm in Figs.8(b)and (c).Pauli exclusion plays a less significant role for larger distances between the charge maxima.Density-functional studies 16,28predict the appearance of interlocked waves of opposite spins in the laboratory frame for long quasi one-dimensional dots.The appear-ance of the spin-density wave for even electron number。