共振能级模型中的全计数统计量
Full Counting Statistics in the Resonant-Level Model
摘要：
在共振能级模型的非平衡定态下，我们导出了大偏差函数，它为电荷转移提供了大时间全计数统计。在自由费米子模型中，这个函数的一般形式是由Levitov和Lesovik在1993年提出的，他们使用了一个特殊的测量装置，包括一个相互作用的自旋。后来有人建议，对于转移电荷的适当量子力学测量也成立。我们给出了一个精确的证明，这两个声明中的共振能级模型。我们首先给出了一个完整的描述模型和它的稳定状态。也就是说，我们解释了如何准备与电荷微分的解耦系统的演变，与杂质耦合，对Hershfield非平衡密度矩阵，在这个意义上的平均值的有限支持运营商。我们描述了这是如何适用于通常的共振能级模型与点状杂质，并为一个正则化的模型与杂质扩散在有限区域，揭示了与点状杂质的微妙之处。然后，我们证明Levitov-Lesovik公式重铸的问题，计算有限支撑的运营商的平均值。
英文摘要：
We derive the large deviation function, which provides the large-time full counting statistics for the charge transfer, in the non-equilibrium steady state of the resonant-level model. The general form of this function in free fermion models, in terms of transmission coefficients, was proposed by Levitov and Lesovik in 1993 using a particular measurement set-up involving an interacting spin. It was later suggested to hold as well for a proper quantum mechanical measurement of the transferred charge. We give a precise proof of both statements in the resonant-level model. We first give a full description of the model and its steady state. That is, we explain how the decoupled system prepared with a charge differential evolves, with the impurity coupling, towards the Hershfield non-equilibrium density matrix, in the sense of averages of finitely-supported operators. We describe how this holds both for the usual resonant-level model with a point-like impurity, and for a regularised model with an impurity spread on a finite region, shedding light on subtleties associated to the point-like impurity. We then prove Levitov-Lesovik formula by recasting the problem into calculating averages of finitely-supported operators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
