孤立量子系统中的概率滞后：从量子观点看不可逆性的微观起始
Probabilistic Hysteresis in an Isolated Quantum System: The Microscopic Onset of Irreversibility from a Quantum Perspective
摘要：
近年来，人们在大粒子数的限制下研究了超冷原子孤立哈密顿系统的概率滞后，在这种情况下，半经典处理是足够的。在这些扫描实验中，控制参数被缓慢地（动态地）来回调整，不可逆性的起源被证明是穿过分界线的来回蓝色通道（可积情况）或进出相空间中混沌海洋的通道（混沌情况）。在这里，我们专注于完整的量子力学描述的可积系统，并显示半经典的结果出现在大粒子数的限制。在相空间中，经典绝热性失效的分界线的交叉，量子系统中不可逆性的起源是绝热能级的一系列避免的交叉：它们变得如此接近，以至于对于适度的粒子数，外部参数的变化已经不切实际地缓慢，以达到完全可逆演化的量子绝热极限。对于一个缓慢的，但有限的扫描速率，我们发现一个广泛的制度，量子结果同意半经典的结果，但只有当除了限制$N\to \infty$的初始系综的状态被认为是具有足够的初始能量宽度。相反，对于单个初始能量本征态，我们发现后向扫描揭示了强的量子效应，即使对于非常大的粒子数。
英文摘要：
Recently probabilistic hysteresis in isolated Hamiltonian systems of ultracold atoms has been studied in the limit of large particle numbers, where a semiclassical treatment is adequate. The origin of irreversibility in these sweep experiments, where a control parameter is slowly (adiabatically) tuned back and forth, turned out to be a passage blue back and forth across a separatrix (integrable case) or a passage in and out of a chaotic sea in phase space (chaotic case). Here we focus on the full quantum mechanical description of the integrable system and show how the semiclassical results emerge in the limit of large particle numbers. Instead of the crossing of a separatrix in phase space, where classical adiabaticity fails, the origin of irreversibility in the quantum system is a series of avoided crossings of the adiabatic energy levels: they become so close that already for modest particle numbers the change of the external parameter has to be unrealistically slow to reach the quantum adiabatic limit of perfectly reversible evolution. For a slow but finite sweep rate we find a broad regime where the quantum results agree with the semiclassical results, but only if besides the limit $N\to \infty$ an initial ensemble of states is considered, with sufficient initial energy width. For a single initial energy eigenstate we find in contrast that the backward sweep reveals strong quantum effects even for very large particle numbers.
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