AI 中文总结
该研究针对正规 Lindblad 生成元的量子轨迹框架，推导稳态平衡关系，证明正规 Lindbladians 排除奇异点，系综平均后恢复独立正交弛豫模式，为 Liouvillian 正规性提供轨迹层面解释。
AI 中文摘要
马尔可夫开放量子系统的高效模拟仍是核心挑战，因为密度矩阵描述随系统大小呈指数增长。量子轨迹方法提供了替代方案，它用随机纯态实现替代混态演化。本文针对正规 Lindblad 生成元研究该框架，其正交本征算子分解排除了瞬态放大。通过将 Lindbladian 分解为确定性平滑项和随机跳变项，我们推导了精确的稳态平衡关系，该关系将这些过程间的相互作用确定为 Liouvillian 正规性的潜在机制。我们进一步证明，正规 Lindbladians 排除了奇异点，且尽管单个量子轨迹通常表现出 Liouvillian 本征模式间的随机耦合，但这些耦合在系综平均后会抵消，恢复出独立的正交弛豫模式。这些结果为 Liouvillian 正规性提供了轨迹层面的解释，并阐明了 Lindblad 生成元的全局性质如何通过随机量子动力学实现。
英文摘要
Efficient simulation of Markovian open quantum systems remains a central challenge because the density-matrix description grows exponentially with system size. Quantum trajectory methods provide an alternative by replacing mixed-state evolution with stochastic pure-state realizations. Here we investigate this framework for normal Lindblad generators, whose orthogonal eigenoperator decomposition precludes transient amplification. By decomposing the Lindbladian into deterministic smooth and stochastic jump contributions, we derive an exact steady-state balance relation that identifies the interplay between these processes as the mechanism underlying Liouvillian normality. We further show that normal Lindbladians exclude exceptional points and that, although individual quantum trajectories generally exhibit stochastic coupling between Liouvillian eigenmodes, these couplings cancel upon ensemble averaging, recovering independent orthogonal relaxation modes. These results provide a trajectory-level interpretation of Liouvillian normality and clarify how a global property of the Lindblad generator is realized through stochastic quantum dynamics.
Comments17 pages, 1 figure
