AI 中文总结
介绍开源Julia包QuantumFCS.jl用于高效灵活的数值FCS计算，通过监测跳跃算符和权重定义电流，实现递归累积量算法，经光子计数和热电流涨落等示例验证，相比现有实现有显著加速。
AI 中文摘要
全计数统计（FCS）为表征量子输运、量子光学和开放量子系统中的电流涨落提供了一个系统框架。我们介绍了这个http URL，一个用于高效灵活的数值FCS计算的开源Julia包。该包通过监测跳跃算符和权重来定义电流，允许在同一工作流程中处理粒子、电和热电流。它实现了一种具有密集、稀疏和迭代求解器后端的递归累积量算法，适用于直接密集方法具有挑战性的模型。我们在接近阻塞击穿相变的驱动耗散Jaynes-Cummings系统中的光子计数以及非线性电路-QED热机中的热电流涨落上演示了该包。这些例子展示了高阶累积量如何揭示亮暗发射之间的间歇性、反聚束，并提供热力学不确定性关系的探针。与现有FCS实现的基准测试显示出显著的加速。
英文摘要
Full-counting statistics (FCS) provides a systematic framework for characterising current fluctuations in quantum transport, quantum optics, and open quantum systems. We introduce QuantumFCSjl, an open-source Julia package for efficient and flexible numerical FCS calculations. The package defines currents through monitored jump operators and weights, allowing particle, electric, and heat currents to be treated within the same workflow. It implements a recursive cumulant algorithm with dense, sparse, and iterative solver backends, making it suitable for models that are challenging for direct dense methods. We demonstrate the package on photon counting in a driven-dissipative Jaynes-Cummings system near the blockade-breakdown phase transition and on heat-current fluctuations in a non-linear circuit-QED heat engine. These examples show how higher cumulants reveal intermittency between bright and dim emission, antibunching, and provide probes of thermodynamic uncertainty relations. Benchmarks against an existing FCS implementation show substantial speed-ups.
Comments34 pages, 7 figures. In this update version we have included mentions to factorial cumulants' helper functions already existing in the API
