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

TL;DR

This paper introduces an efficient, mesh-free Frozen Gaussian Sampling algorithm for simulating open quantum systems in the semiclassical regime, overcoming computational and stability challenges of traditional methods.

Contribution

The paper presents a novel FGS algorithm that is independent of the semiclassical parameter and eliminates boundary instabilities, enabling long-time simulations of open quantum systems.

Findings

Sampling error is independent of the semiclassical parameter.

Eliminates boundary-induced instabilities in long-time simulations.

Provides numerical evidence for steady states in non-harmonic potentials.

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.