量子相空间中的概率滞后
Probabilistic Hysteresis from a Quantum Phase Space Perspective
摘要：
\emph{Probabilistic hysteresis}是一个小的，孤立的经典系统中的不可逆性的表现[Sci. Rep. 9，14169]：在控制参数的缓慢循环扫描之后，微正则系综返回到其初始能量的邻域的概率显著低于1。最近在粒子数不太小的量子系统$N$中证实了类似的现象。然而，量子-经典对应在这种情况下被发现是不平凡的;控制参数变化的速率不能太慢，能量的初始分布不能太窄。本文利用Husimi量子相空间形式直接比较了概率滞后的量子形式和经典形式。特别是，我们证明了经典的遍历机制，这是一个关键因素，在经典的概率滞后，可以导致量子经典对应的故障，而不是量子遍历。因此，尽管运动方程中的量子修正与$1/N$成正比，因此看起来很小，但长期演化中存在着强量子效应。然而，我们还表明，量子遍历恢复平均能量，使足够的初始能量宽度和不太慢的扫描速率的经典结果恢复毕竟。最后，我们表明，在我们的系统中的经典和绝热极限，导致量子-经典对应的准静态极限的故障，是由于宏观量子隧穿通过一个大的能量势垒的形式不可解释性。这解释了在我们以前的工作中报道的达到量子绝热极限所需的极慢的扫描速率。
英文摘要：
\emph{Probabilistic hysteresis} is a manifestation of irreversibility in a small, isolated classical system [Sci. Rep. 9, 14169]: after a slow cyclic sweep of a control parameter, the probability that a microcanonical ensemble returns to the neighborhood of its initial energy is significantly below one. A similar phenomenon has recently been confirmed in a corresponding quantum system for not too small particle number $N$. Quantum-classical correspondence has been found to be non-trivial in this case, however; the rate at which the control parameter changes must not be extremely slow and the initial distribution of energies must not be too narrow. In this paper we directly compare the quantum and classical forms of probabilistic hysteresis by making use of the Husimi quantum phase space formalism. In particular we demonstrate that the classical ergodization mechanism, which is a key ingredient in classical probabilistic hysteresis, can lead to a breakdown of quantum-classical correspondence rather than to quantum ergodization. As a result strong quantum effects in the long-term evolution are present, even though the quantum corrections in the equations of motion are proportional to $1/N$ and therefore would naively seem to be small. We also show, however, that quantum ergodization is restored by averaging over energies, so that for sufficient initial energy width and not-too-slow sweep rate the classical results are recovered after all. Finally we show that the formal incommutability of the classical and adiabatic limits in our system, leading to the breakdown of quantum-classical correspondence in the quasi-static limit, is due to macroscopic quantum tunneling through a large energetic barrier. This explains the extremely slow sweep rates needed to reach the quantum adiabatic limit that were reported in our previous work.
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