Transient fluctuation relations for time-dependent particle transport
Transient fluctuation relations for time-dependent particle transport
复制标题
随时间变化的粒子输运的瞬态涨落关系
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
B. Narozhny
中科院分区：
文献类型：
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作者：
A. Altland;A. D. Martino;R. Egger;B. Narozhny
我们考虑在时变驱动力的影响下的粒子输运，其中涨落关系连接着物理可观测量的时间逆演化对的统计量。在许多“介观”输运过程中，有效的多粒子动力学主要是经典的，而控制粒子运动的微观速率是量子力学的起源。在此，我们使用随机路径积分方法作为一种最佳工具来探索此类应用中的涨落统计。描述凯尔德什量子非平衡场理论的经典极限的随机路径积分封装了微观粒子交换率的量子起源。在动力学上，它等同于一个传输主方程，它是一种足够普遍的形式，足以描述许多实际感兴趣的应用。应用随机路径积分，导出了由时变力引起的水流的一般泛函涨落关系。我们表明，这种设置所隐含的连续测量过程并不会危及量子涨落关系的推导。虽然在许多情况下，全时变电流分布的涨落关系可能包含过多的信息，但我们推导了一些简化的关系，并展示了它们在介观输运中的应用。例如传输电荷的分布，其中我们表明，波动关系的推导需要对电荷和功的统计进行联合监测。
We consider particle transport under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time reversed evolutions of physical observables. In many "mesoscopic" transport processes, the effective many-particle dynamics is dominantly classical, while the microscopic rates governing particle motion are of quantum-mechanical origin. We here employ the stochastic path integral approach as an optimal tool to probe the fluctuation statistics in such applications. Describing the classical limit of the Keldysh quantum nonequilibrium field theory, the stochastic path integral encapsulates the quantum origin of microscopic particle exchange rates. Dynamically, it is equivalent to a transport master equation which is a formalism general enough to describe many applications of practical interest. We apply the stochastic path integral to derive general functional fluctuation relations for current flow induced by time-varying forces. We show that the successive measurement processes implied by this setup do not put the derivation of quantum fluctuation relations in jeopardy. While in many cases the fluctuation relation for a full time-dependent current profile may contain excessive information, we formulate a number of reduced relations, and demonstrate their application to mesoscopic transport. Examples include the distribution of transmitted charge, where we show that the derivation of a fluctuation relation requires the combined monitoring of the statistics of charge and work.