论文标题
嘈杂的介质系统，开放量子SSEP和自由概率的相干波动
Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
论文作者
论文摘要
量子相干表征颗粒在某些给定距离内机械干扰的能力。在嘈杂的多体量子系统的背景下，这些相干可能会波动。一个简单的玩具模型是在平衡设置中研究此类波动的一个简单的玩具模型是开放的量子对称简单排除过程（Q-SSEP），该过程描述了在两个储层之间耦合的随机振幅的一个维度中的无旋转费用。在这里，我们表明Q-SESP中连贯性波动的动力学具有自然解释为自由累积物，这是自由概率理论的概念。基于这种见解，我们提供了启发式论点，为什么我们期望自由概率理论是一个适当的框架，以描述通用介观系统中的连贯波动，在这些框架中，噪声从粗糙的描述中出现。在Q-SSEP的情况下，我们展示了如何使用与自由概率理论的链接来得出连接连接波动的时间演变以及简单的稳态解决方案。
Quantum coherences characterise the ability of particles to quantum mechanically interfere within some given distances. In the context of noisy many-body quantum systems these coherences can fluctuate. A simple toy model to study such fluctuations in an out-of-equilibrium setting is the open quantum symmetric simple exclusion process (Q-SSEP) which describes spinless fermions in one dimension hopping to neighbouring sites with random amplitudes coupled between two reservoirs. Here we show that the dynamics of fluctuations of coherences in Q-SSEP have a natural interpretation as free cumulants, a concept from free probability theory. Based on this insight we provide heuristic arguments why we expect free probability theory to be an appropriate framework to describe coherent fluctuations in generic mesoscopic systems where the noise emerges from a coarse-grained description. In the case of Q-SSEP we show how the link to free probability theory can be used to derive the time evolution of connected fluctuations of coherences as well as a simple steady state solution.
