初微正则和能量本征态的功概率分布的刚性和Jarzynski关系
Stiffness of Probability Distributions of Work and Jarzynski Relation for Initial Microcanonical and Energy Eigenstates
摘要：
我们考虑封闭的量子系统（浴可以集成到其中），其被驱动，即，服从随时间变化的汉密尔顿。作为一个出发点，我们假设，在某些能量的微正则态初始化的系统，由此产生的概率密度的工作（工作PDF）在很大程度上是独立的这些特定的初始能量。我们分析表明，这种假设的“刚度”，再加上假设的能量本征态的密度呈指数增长，是足够的，但不是必要的有效性的Jarzynski关系（JR）上述微正则初始状态。即使在没有微观可逆性的情况下，这也是成立的。要仔细检查刚度和JR的微正则初始状态之间的连接，我们进行数值分析的系统，包括随机矩阵，可以从刚性到非刚性。在这些例子中，我们发现，在存在刚性的情况下，JR得到满足，而在不存在刚性的情况下，JR被违反，这表明刚性和JR之间存在非常密切的联系。值得注意的是，在大系统的极限，我们发现JR满足，即使是纯初始能量本征态。由于这在经典系统中没有类似物，我们认为这是一个真正的量子现象。
英文摘要：
We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. As a starting point we assume that, for systems initialized in microcanonical states at some energies, the resulting probability densities of work (work-PDFs) are largely independent of these specific initial energies. We show analytically that this assumption of "stiffness", together with the assumption of an exponentially growing density of energy eigenstates, is sufficient but not necessary for the validity of the Jarzynski relation (JR) for the above microcanonical initial states. This holds, even in the absence of microreversibility. To scrutinize the connection between stiffness and the JR for microcanonical initial states, we perform numerical analysis on systems comprising random matrices which may be tuned from stiff to nonstiff. In these examples we find the JR fulfilled in the presence of stiffness, and violated in its absence, which indicates a very close connection between stiffness and the JR. Remarkably, in the limit of large systems, we find the JR fulfilled, even for pure initial energy eigenstates. As this has no analogue in classical systems, we consider it a genuine quantum phenomenon.
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