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

Abstract

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.

Comments: 34 pages, 7 figures, open-access code available via https://doi.org/10.5281/zenodo.3744460