Frozen Gaussian sampling algorithms for simulating Markovian open quantum systems in the semiclassical regime

• URL: http://arxiv.org/abs/2512.14015v1
• Date: Tue, 16 Dec 2025 02:21:34 GMT
• Title: Frozen Gaussian sampling algorithms for simulating Markovian open quantum systems in the semiclassical regime
• Authors: Limin Xu, Zhen Huang, Zhennan Zhou,
• Abstract summary: This paper introduces an efficient Frozen Gaussian Sampling (FGS) algorithm based on the Wigner-Fokker-Planck phase-space formulation.<n>Its sampling error is independent of the semiclassical parameter $varepsilon$, thus breaking the prohibitive computational scaling faced by grid methods in the semiclassical limit.<n>We provide compelling numerical evidence for the existence of steady states in strongly non-harmonic potentials-a regime where rigorous analytical results are currently lacking.
• Score: 4.655774822811101
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating Markovian open quantum systems in the semiclassical regime poses a grand challenge for computational physics, as the highly oscillatory nature of the dynamics imposes prohibitive resolution requirements on traditional grid-based methods. To overcome this barrier, this paper introduces an efficient Frozen Gaussian Sampling (FGS) algorithm based on the Wigner-Fokker-Planck phase-space formulation. The proposed algorithm exhibits two transformative advantages. First, for the computation of physical observables, its sampling error is independent of the semiclassical parameter $\varepsilon$, thus fundamentally breaking the prohibitive computational scaling faced by grid methods in the semiclassical limit. Second, its mesh-free nature entirely eliminates the boundary-induced instabilities that constrain long-time grid-based simulations. Leveraging these capabilities, the FGS algorithm serves as a powerful investigatory tool for exploring the long-time behavior of open quantum systems. Specifically, we provide compelling numerical evidence for the existence of steady states in strongly non-harmonic potentials-a regime where rigorous analytical results are currently lacking.

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