小马尔可夫系统中电流累积量的精确计算

非马尔可夫量子随机过程的计数统计

Counting Statistics of Non-Markovian Quantum Stochastic Processes

本文导出了非马尔可夫量子随机输运过程的累积生成函数的一般表达式。CGF的长时间限制由记忆核的预解式的单个主导极点确定，我们使用递归方案从记忆核提取电流的零频率累积量。有限频率噪声不仅用预解式表示，而且用初始系统-环境相关性表示。作为一个说明性的例子，我们考虑了电子输运通过一个耗散的双量子点，我们研究了耗散对高阶零频累积量和有限频率噪声的影响。

分子系统波包动力学密度矩阵方法中的累积展开法

Cumulant expansion method in the density matrix approach to wave packet dynamics in molecular systems

利用累积展开法得到了分子与热浴相互作用的非马尔可夫主方程。将该方程应用于分子波包弛豫动力学问题。精确解证明了波包演化的经典压缩和热浴相关的频移。

Zero-Crossing Statistics for Non-Markovian Time Series

In applications spaning from image analysis and speech recognition, to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging. And therefore, few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero-crossings in a fixed time interval of a zero-mean Gaussian stationary processes. In this study we use the so-called Indepe…

Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics

Stochastic Thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from anti-symmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic …

非平衡小系统电流累积量的计算

Computation of current cumulants for small nonequilibrium systems

我们分析了一个系统的算法的精确计算的当前累积量的随机非平衡系统，最近讨论的框架内的全计数统计介观系统。这种方法是基于识别当前累积量从瑞利-薛定谔微扰展开的生成函数。这里，它是来自一个简单的路径分布的身份，并扩展到多个电流的联合统计。对于一个可能的物理解释，我们比较这种方法的广义Onsager-Machlup形式主义。我们目前的计算边界驱动川崎动力学的一维链，吸引和排斥粒子相互作用。

累积量演化与全计数统计的高效计算：应用于无限温度量子自旋链

Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains

提出高效计算量子生成函数的方法，用于高温一维量子系统，在自旋1/2各向异性海森堡链上达到前所未有的时间尺度，挑战KPZ普适性猜想。