Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator

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