Weakly Non-Ergodic Statistical Physics
Weakly Non-Ergodic Statistical Physics
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DOI：
10.1007/s10955-008-9610-3
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发表时间：
2008-11-01
影响因子：
1.6
通讯作者：
Barkai, E.
中科院分区：
文献类型：
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作者：
Rebenshtok, A.;Barkai, E.
对于弱非遍历系统，杆上时间平均可观(O)的概率密度函数为fα((O)on bar)=1/pi Lim(epsilon-gt；0)Im Sigma(L)(j=1)P-j(Eq)((O)over bar-O-j+i epsilon)(α-1)/Sigma(L)(j=1)P-j(Eq)(O)over bar-O-j+i epsilon)(α)其中O-j是系统在状态j=1时的可观测值。L.p(J)(Eq)j是系统系综中的一个成员占据平衡状态j的概率。对于在结合力场中经历分数扩散过程的粒子，在热平衡条件下，p(J)(Eq)是玻耳兹曼正则概率。在无偏次扩散连续时间随机游走模型中，指数0<；α<；1是类似于自由边界条件下的t(α)的反常扩散指数<；x(2)>；。当恢复α->1遍历统计力学时，LIM(α->1)f(α)(杆上的(O))=杆上的增量((O))。我们简要讨论了单粒子实验中可能的物理应用。
For weakly non ergodic systems, the probability density function of a time average observable (O) over bar is f alpha((O) over bar) = 1/pi lim(epsilon -> 0) Im Sigma(L)(j=1) P-j(eq) ((O) over bar -O-j+i epsilon)(alpha-1)/Sigma(L)(j=1) P-j(eq)((O) over bar -O-j+i epsilon)(alpha) where O-j is the value of the observable when the system is in state j = 1,... L. p(j)(eq) j is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p(j)(eq) is Boltzmann's canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0 < alpha < 1 is the anomalous diffusion exponent < x(2)> similar to t(alpha) found for free boundary conditions. When alpha -> 1 ergodic statistical mechanics is recovered lim(alpha -> 1) f(alpha)((O) over bar) = delta((O) over bar - < O >). We briefly discuss possible physical applications in single particle experiments.