利用大数定律证明广义热化定理 CQ,nO<m甲2=∑ )8n2 )+1(E,o) )+(E,) ∑|C(n,n)P=1 Cn,)的平均值是 日④O,n ‖,日 1D①xn为息 甸之 D,(E, ∑|ΦnnXn ∑ D(E-no, 8 Inn nD+1(E,6) ITP
利用大数定律证明广义热化定理 |n nj→En, Cn, nj j1 N |nj , | 1 | | ( , ) E n n N n D E = + ||n|| 2 nj→En, |Cn, nj| 2 , 2 1 [ , ] 1 | ( , ) | 1, ( , ) j E j N n n C n n D E + = ||n|| 2 nj→En, 1 DNE n, 2 , , 1 1 1 (| |) || || | | ( , ) ( , ) | | ( , ) S B E E n N n N n N Tr n n D E D E n n n D E + + = = − = 2 | ( , ) | 1 C n nj 的平均值是
明显考虑相互作用 H Dong(ILi), S. Yang, X F Liu,, C P. Sun, quant-ph/0207027 H=mb+00a+b2∑[8a+he YB Gao,C.P.sun,PRE,75,011105(2007) ({3})=(m-7)0+n,h个身国h∠Q 4为y In (n=d(ain)ai o=d(am)n, y ITP
明显考虑相互作用 H. Dong (董辉), S. Yang, X.F. Liu, , C.P. Sun , quant-ph/0207027 . j j j j j j j H b b a a b b g a h c + + + = + + + Y.B Gao , C.P. Sun , PRE, 75, 011105 (2007) 2 ( { }) ( ) j j j j e n n n n n = − + |nnjn |n j1 N |njn j gj 2 4j ! 1 | ( ) ( ) | 0 ( ) | n j jn j j jn j j n n D a D n n + = =
相互作用诱发能壳变形 (E+o)/1 无相互作用 能壳变形 do+(n-kn)o=E n@+(n-kn yo=E n@+no=E n@+no=E+8 VE=VE(6): in(n, >E(n-Kn)o+ 2o, sE+6) ITP
相互作用诱发能壳变形 2 1 ( ) :{| { } | ( ) } N E E j j j j V V n n E n n n E = = − + + 无相互作用 能壳变形
模型的普适性 In the weak coupling limit, any heat bath could be universal modeled as a collection of harmonic oscillators with the linear couplings to the surrounded system accordingly A.O. Caldiera, A.J. Leggett, Ann. Phys.(NY)149, 374(1983) M-level system H, =2 Inn (g, a*+Hc ) E E,(K)+ ∑ EK 力g/(纵 ITP
模型的普适性 A. O. Caldiera , A. J. Leggett, Ann. Phys. (NY) 149, 374(1983). In the weak coupling limit, any heat bath could be universally modeled as a collection of harmonic oscillators with the linear couplings to the surrounded system accordingly. | |( H.c.), , = + + H n n n g j a j n M-level system I ( ) ( ) j j N j E n nj n n = = + 1 ,{ } ( ) 2 n n n = − j |gj | 2 /4j