周期驱动Lindblad方程的异常点和指数灵敏度

IF 1.3 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Open Systems & Information Dynamics Pub Date : 2023-06-01 DOI:10.1142/S1230161223500087
J. Larson, Sofia Qvarfort
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引用次数: 0

摘要

在此贡献的纪念问题Göran Lindblad,我们研究周期驱动的Lindblad方程为一个两能级系统。我们使用绝热对角化和时间演化的数值模拟以及Floquet理论对系统进行了分析。绝热对角化揭示了系统中异常点的存在,异常点取决于系统参数。我们展示了这些异常点的存在如何影响系统演化,导致这些点的快速减相和阶梯状的相干性丧失。这种现象可以通过测量实验观察到,例如,人口反转。我们还观察到异常点的存在似乎与系统支持的基础李代数有关。在Floquet分析中,我们将时变Liouvillian映射为非厄米Floquet hamilton,并分析其谱。对于弱衰减率,我们发现了伴随相应的stark局域本征态的wanner - stark阶梯谱。对于较大的衰减率,阶梯开始溶解,新的、局部化程度较低的状态出现。此外,它们的特征值对扰动呈指数级敏感,类似于在某些非厄米哈密顿量中发现的趋肤效应。
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Exceptional Points and Exponential Sensitivity for Periodically Driven Lindblad Equations
In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.
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来源期刊
Open Systems & Information Dynamics
Open Systems & Information Dynamics 工程技术-计算机:信息系统
CiteScore
1.40
自引率
12.50%
发文量
4
审稿时长
>12 weeks
期刊介绍: The aim of the Journal is to promote interdisciplinary research in mathematics, physics, engineering and life sciences centered around the issues of broadly understood information processing, storage and transmission, in both quantum and classical settings. Our special interest lies in the information-theoretic approach to phenomena dealing with dynamics and thermodynamics, control, communication, filtering, memory and cooperative behaviour, etc., in open complex systems.
期刊最新文献
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