论文标题
初始微型和能量特征状态的工作和Jarzynski关系的概率分布的刚度
Stiffness of Probability Distributions of Work and Jarzynski Relation for Initial Microcanonical and Energy Eigenstates
论文作者
论文摘要
我们考虑被驱动的封闭量子系统（可以集成在哪些浴场中），即受时间依赖的汉密尔顿人。作为起点，我们假设对于以某些能量初始初始化的微型态状态初始化的系统，所得的工作概率密度（Work-PDF）在很大程度上与这些特定的初始能量无关。我们分析地表明，这种“刚度”的假设以及能量特征态密度呈指数增长的假设足够，但对于上述微跨初始状态而言，Jarzynski关系（JR）的有效性并不是必需的。即使在没有微可逆性的情况下，这也是如此。为了仔细检查刚度与JR之间的微观初始状态之间的连接，我们对包含随机矩阵的系统进行数值分析，这些矩阵可能会从刚性到非势头调整。在这些示例中，我们发现在存在刚度的情况下实现了JR，并在其缺乏的情况下违反了，这表明刚度与JR之间的联系非常紧密。值得注意的是，在大型系统的极限中，我们发现JR满足，即使对于纯的初始能量本征态也是如此。由于这在古典系统中没有类似物，因此我们认为这是一种真正的量子现象。
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.
