Potential renormalisation, Lamb shift and mean-force Gibbs state – to shift or not to shift?

IF 5.1 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Quantum Pub Date : 2025-09-30 DOI:10.22331/q-2025-09-30-1868
Luis A. Correa, Jonas Glatthard
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引用次数: 0

Abstract

Often, the microscopic interaction mechanism of an open quantum system gives rise to a `counter term' which renormalises the system Hamiltonian. Such term compensates for the distortion of the system's potential due to the finite coupling to the environment. Even if the coupling is weak, the counter term is, in general, not negligible. Similarly, weak-coupling master equations feature a number of `Lamb-shift terms' which, contrary to popular belief, cannot be neglected. Yet, the practice of vanishing both counter term and Lamb shift when dealing with master equations is almost universal; and, surprisingly, it can yield $better$ results. By accepting the conventional wisdom, one may approximate the dynamics more accurately and, importantly, the resulting master equation is guaranteed to equilibrate to the correct steady state in the high-temperature limit. In this paper we discuss why is this the case. Specifically, we show that, if the potential distortion is small – but non-negligible – the counter term does not influence any dissipative processes to second order in the coupling. Furthermore, we show that, for large environmental cutoff, the Lamb-shift terms approximately cancel any coherent effects due to the counter term – this renders the combination of both contributions irrelevant in practice. We thus provide precise conditions under which the open-system $folklore$ regarding Lamb shift and counter terms is rigorously justified.
潜在重整,兰姆位移和平均力吉布斯态,移动还是不移动?
通常,开放量子系统的微观相互作用机制会产生一个“反项”,使系统哈密顿量重新规范化。这一项补偿了由于系统与环境的有限耦合而造成的系统势能的畸变。即使耦合很弱,反项通常也是不可忽略的。类似地,弱耦合主方程具有许多“兰姆移项”,与流行的看法相反,它们不能被忽视。然而,在处理主方程时,消除反项和兰姆位移的做法几乎是普遍的;而且,令人惊讶的是,它可以产生更好的结果。通过接受传统的智慧,人们可以更准确地近似动力学,重要的是,得到的主方程保证在高温极限下平衡到正确的稳态。在本文中,我们讨论了为什么会出现这种情况。具体地说,我们表明,如果潜在畸变很小-但不可忽略-反项不影响耦合中的任何二阶耗散过程。此外,我们表明,对于大的环境截止,兰姆移位项近似地抵消了由于反项而产生的任何相干效应-这使得两者的组合在实践中无关紧要。因此,我们提供了精确的条件,在这些条件下,关于兰姆移位和反项的开放系统$folklore$是严格合理的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Quantum
Quantum Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
9.20
自引率
10.90%
发文量
241
审稿时长
16 weeks
期刊介绍: Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.
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