从量子信息观点看量子统计和热力学.ppt

2.信息擦除、麦克斯韦妖与量子热机
H. Quan, Y. Wang, Y Liu, CPS, F. Nori Phys. Rev. Lett. 97, 180402(2006) H. T. Quan, P. Zhang, CPS, Phys. Rev. E 73, 036122 (2006)
3. 量子控制、纳米机械及其它
QPQIP in ITP CAS
Previous Members: Dr. Y.X. Liu, (Riken) Dr. P. Zhang, (Georgia Tech) Dr. Yong Li , (Basel) Dr. Y. D. Wang, (NTT)
Dr. F. Xue, (Riken)
Dr. Y.B. Gao (BPTU) Prof. Sixia Yu (UCST) Prof. Xiaoguang Wang (ZJU )
N
n| |n j n j| |n
n 1 nj E n j
微正则系综
N
正则系综
S TrE ( ) m j | ( E , ) | m j
{m j } j 1 N 1 | n n | (m j , n j ) DN 1 ( E , ) n {m j }[ n j ]E n j 1

1 1 | n n | [ m源自文库 DN 1 ( E , ) n j ]E n
n

DN ( E n , ) | n n | Pn ( ) | n n | DN 1 ( E , ) n
统计熵
S ( E) : ln[ DN ( E, )]
热力学极限
P. Zhang, Y. Wang, CPS, Phys. Rev. Lett . 95, 097204 (2005 ) F. Xue, L. Zhong, Yong Li, and CPS, Phys. Rev. B 75, 033407 (2007)
Quantum Physics and Quantum Information Processing
| n | n j
j 1
N
S TrB (| E , E , |)
n
DN ( E n, ) | n n | DN 1 ( E , )
Based on The Law of Large Numbers (大数定律)
S. Popescu et al , Nature Physics 2, 754 (2006) S. Goldstein et al., Phys. Rev. Lett. 96, 050403 (2006)
| E ,
[ n , n j ]E ,

C (n, n j ) DN 1 ( E, )
dS ( E ) dE
e n
n P ( ) e n
广义热化定理
Generalized Thermalization
Almost all the pure states of the “Universe ” can give the Canonic Equilibrium State by tracing over the Environment
DN ( E, ) DN 1 ( E, )
n
S ( E n ) S ( E )
E
P n ( )
dS ( E ) n dE S ( E ) n
DN ( E n , ) DN 1 ( E , )
DN 1 ( E n , ) DN 1 ( E , )
H. Dong, S. Yang, X.F. Liu, , CPS , 2007 H. Quan, Z. Song, X. Liu, P. Zanardi, CPS , Phys. Rev. Lett. 96, 140604 (2006) Y. B. Gao and CPS, Phys. Rev. E 75, 011105 (2007)
Sub Energy Shell
E
E En
E En
热库的约束

E
E En j E En
j 1
N
E,

1 D N E, 1 1 D N E, 1
n| |n j n j| |n
n,n j E, j 1 N
Present Members Dr. Lan Zhou Hai-Tao Quan Liang He, Zi-Ri Gong Hui Dong, Tao Shi Shuo Yang, Jing-Ning Zhang Prof. Su YI Prof. Chang-Pu Sun
Main Collaborators: Prof. Zi Song (Nankai), Prof. Xue-Feng Liu (PKU), Prof. Franco Nori (UM , Riken) Prof. Paolo Zanardi (ISI), Prof. J.Q. You (Fudan) Prof. Li You (Georgia Tech)
从量子信息观点看量子统计和热力学
孙昌璞 中国科学院理论物理研究所
http://power.itp.ac.cn/~suncp/quantum.htm
1.量子纠缠与量子统计力学的基础
Temperature and Quantum Phase transition emerge due to entanglement
等几率假设
统
计
力
学
微正则、正则系综
等几率假设
？
统计物理基础
平衡态情况 等几率假说 对应于相同的宏观量（能量 E）的 态中每个态出现的几率相等
( E, )
微观

E
E
P
1 ( E , )
E En j E
j 1
N
Energy Shell
微正则系综密度矩阵