The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved by benchmarking quantum dynamics of few-body systems against independent exact solutions. A diffusion gauge is implemented here as a so-called noise-matrix, which satisfies a matrix equation defined by the corresponding Fokker--Planck equation of the phase-space representation. For the physical systems with fermionic particles considered here, the numerical evaluation of the new diffusion gauges allows us to double the practical simulation time, compared with hitherto known analytic noise-matrices. This development may have far reaching consequences for future quantum dynamical simulations of many-body systems.

翻译：高斯相空间表示可用于数值实现费米子粒子的量子动力学。为改进数值结果，我们在此类实现中探索动态扩散规范的使用。这是通过将少体系统的量子动力学与独立精确解进行基准测试来实现的。扩散规范在此实现为所谓的噪声矩阵，该矩阵满足由相应相空间表示的福克-普朗克方程定义的矩阵方程。对于本文考虑的含费米子粒子的物理系统，与迄今为止已知的解析噪声矩阵相比，新扩散规范的数值评估使我们能够将实际模拟时间延长一倍。这一进展可能对未来的多体系统量子动力学模拟产生深远影响。