开放量子系统主方程的不连续伽辽金格式

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-08-05 DOI:10.1016/j.cpc.2025.109778

José A. Morales Escalante

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引用次数: 0

摘要

本文提出了一种不连续伽辽金（DG）方法的数值分析，该方法用于转换主方程来模拟一个开放量子系统：一个与噪声环境相互作用的量子子系统。结果表明，对于非谐波势的一般情况下，与采用DG格式的相同系统的Wigner-Fokker-Planck模型相比，所提出的变换后的主方程具有更低的计算成本。给出了在位置基上由Lindblad主方程得到的适合于对流扩散方程组的不连续伽辽金（DG）数值格式的特点。这使我们可以通过计算来解决对开放量子系统问题建模的变换后的系统。然后给出了谐波势的基准情况，并将其数值结果与该问题的解析稳态解进行了比较。然后提出了两种非谐波情况：线性势和四次势通过我们的DG框架建模，并给出了我们的数值结果。

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Discontinuous Galerkin schemes for master equations modeling open quantum systems

This work presents a numerical analysis of a Discontinuous Galerkin (DG) method for a transformed master equation modeling an open quantum system: a quantum sub-system interacting with a noisy environment. It is shown that the presented transformed master equation has a reduced computational cost in comparison to a Wigner-Fokker-Planck model of the same system for the general case of non-harmonic potentials via DG schemes. Specifics of a Discontinuous Galerkin (DG) numerical scheme adequate for the system of convection-diffusion equations obtained for our Lindblad master equation in position basis are presented. This lets us solve computationally the transformed system of interest modeling our open quantum system problem. The benchmark case of a harmonic potential is then presented, for which the numerical results are compared against the analytical steady-state solution of this problem. Two non-harmonic cases are then presented: the linear and quartic potentials are modeled via our DG framework, for which we show our numerical results.

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.