发表机构
National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对开放量子系统模拟中通用数值方法的挑战，提出确定性多项式混沌伽辽金方法，可降低计算成本、消除统计误差，且在挑战性问题上表现优异。
AI 中文摘要
开发非马尔可夫量子态扩散的通用数值方法，长期以来一直是开放量子系统模拟领域的一项挑战。本文提出一种确定性多项式混沌伽辽金方法，该方法易于实现、精度高且效率高。通过将环境关联的低秩分解与多项式混沌基上的伽辽金投影相结合，该方法得到一种确定性公式，可与标准偏微分方程数值求解器兼容。约化密度矩阵可通过单次确定性求解得到，其计算成本与计算一条随机层次轨迹的成本相当。因此，替换$N_{\text{traj}}$条轨迹的集合可将计算成本降低约$N_{\text{traj}}$倍，并消除统计采样误差。基准比较表明，所提方法与测试的随机层次方法相比，在更低计算成本下实现了更小的误差。涉及非二次势、衍射与干涉以及耦合三维动力学的应用，证明了其处理挑战性问题的能力。
英文摘要
Developing general-purpose numerical methods for non-Markovian quantum state diffusion has long been a challenge in the simulation of open quantum systems. This paper proposes a deterministic polynomial chaos Galerkin method, which is easy to implement, accurate, and efficient. By combining a low-rank decomposition of bath correlations with Galerkin projection onto a polynomial chaos basis, the method yields a deterministic formulation compatible with standard numerical solvers for partial differential equations. The reduced density matrix is obtained from a single deterministic solve at a cost comparable to that of computing one stochastic hierarchy trajectory. Replacing an ensemble of $N_{\mathrm{traj}}$ trajectories therefore reduces the computational cost by approximately a factor of $N_{\mathrm{traj}}$ and eliminates statistical sampling error. Benchmark comparisons show that the proposed method achieves smaller errors at lower computational cost than the tested stochastic hierarchy methods. Applications involving nonquadratic potentials, diffraction and interference, and coupled three-dimensional dynamics demonstrate its ability to handle challenging problems.
