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

Highlights

• New difference operator with continuum property: neutrality under coordinate transformation $(x,y)\to (z=x-y,z^{\prime }=x+y)$.

• First direct simulation of the high temperature Lindblad equation for quarkonium particles with exact trace preservation.

Abstract

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.