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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:425

Article

Alund, Oskar¹  Akamatsu, Yukinao²  Lauren, Fredrik¹  Miura, Takahiro²  Nordstrom, Jan^1,3  Rothkopf, Alexander⁴ 

[1] Linkoping Univ, Dept Math, Computat Math, SE-58183 Linkoping, Sweden

[2] Osaka Univ, Dept Phys, Toyonaka, Osaka 5600043, Japan

[3] Univ Johannesburg, Dept Math & Appl Math, POB 524, ZA-2006 Auckland Pk, South Africa

[4] Univ Stavanger, Fac Sci & Technol, N-4021 Stavanger, Norway

关键词: Time integration;    Initial boundary value problems;    Dissipative systems;    Open quantum systems;    Summation-by-parts operators;    Mimetic operator;   

DOI  :  10.1016/j.jcp.2020.109917

来源: Elsevier

【 摘 要 】

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 (RNSBP) operator enables an accurate simulation of the full dissipative dynamics of this open quantum system. (c) 2020 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

【 授权许可】

Free