On the uniqueness of the steady-state solution of the Lindblad-Gorini- Kossakowski-Sudarshan equation
On the uniqueness of the steady-state solution of the Lindblad-Gorini- Kossakowski-Sudarshan equation
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DOI：
10.1088/1742-5468/ab0c1c
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发表时间：
2019-04-01
影响因子：
2.4
通讯作者：
Nigro, Davide
中科院分区：
文献类型：
--
作者：
Nigro, Davide
本文的目的是双重的。第一个目的是简要回顾有关Lindblad-Gorini-Kossakowski-Sudarshan主方程稳态解的唯一性和保证动态半群的松弛性和不可约性的判据的最相关的理论结果。特别地，我们通过考虑它们对最简单的开放量子系统（即在零温度下耦合到谐振子浴的两能级系统）特征的适用性来测试和讨论它们的物理意义。第二个目标是提供一组保证稳态解的唯一性及其吸引性的充分条件。从简单的假设出发，我们推导出简单的标准，可以有效地利用这些标准来表征自旋和玻色子（具有截断的Fock空间）的耗散系统的行为，以及最近研究的各种其他开放量子系统。
The aims of this paper are twofold. The first aim is to give a brief review of the most relevant theoretical results concerning the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan master equation and the criteria which guarantee relaxingness and irreducibility of dynamical semigroups. In particular, we test and discuss their physical meaning by considering their applicability to the characterisation of the simplest open quantum system i.e. a two-level system coupled to a bath of harmonic oscillators at zero temperature. The second aim is to provide a set of sufficient conditions which guarantees the uniqueness of the steady-state solution and its attractivity. Starting from simple assumptions, we derive simple criteria that can be efficiently exploited to characterise the behavior of dissipative systems of spins and bosons (with truncated Fock space), and a wide variety of other open quantum systems recently studied.