We develop a novel numerical scheme for the simulation of dissipative quantum dynamics, following from two-body Lindblad master equations. It exactly preserves the trace of the density matrix and shows only mild deviations from hermiticity and positivity, which are the defining properties of the continuum Lindblad dynamics. The central ingredient is a new spatial difference operator, which not only fulfills the summation by parts (SBP) property, but also implements a continuum reparametrization property. Using the time evolution of a heavy-quark anti-quark bound state in a hot thermal medium as an explicit example, we show how the reparametrization neutral summation-by-parts (RN-SBP) operator enables an accurate simulation of the full dissipative dynamics of this open quantum system.

我们从二体Lindblad主方程出发，开发了一种用于耗散量子动力学仿真的新颖数值方案。它精确地保留了密度矩阵的痕迹，并且仅显示出与遗传度和正性的温和偏差，这是连续林德布拉德动力学的定义性质。中心要素是一个新的空间差算子，它不仅满足分部求和（SBP）属性，而且实现了连续统重新参数化属性。以热介质中重夸克反夸克束缚态的时间演化为例，我们展示了重新参数化中性部分求和（RN-SBP）算子如何精确模拟整个耗散动力学这个开放量子系统。