基于新的重参数化中性分部分求和差分算子的保迹量子动力学
Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator
摘要：
我们发展了一种新的数值方案，用于模拟耗散量子动力学的两体Lindblad主方程。所有定义的Lindblad动力学，厄米性，积极性，特别是迹守恒的演变密度矩阵的连续属性被保留。中心成分是一种新的空间差分算子，它不仅满足部分求和（SBP）性质，而且还实现了连续统重新参数化性质。作为一个明确的例子，在一个热的热介质中的重夸克反夸克束缚态的时间演化，我们展示了如何重新参数化中性求和部分（RN-SBP）运营商保持连续性的理论。
英文摘要：
We develop a novel numerical scheme for the simulation of dissipative quantum dynamics following from two-body Lindblad master equations. All defining continuum properties of the Lindblad dynamics, hermiticity, positivity and in particular trace conservation of the evolved density matrix are preserved. The central ingredient is a new spatial difference operator, which not only fulfils 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 preserves the continuum properties of the theory.
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