{"title":"潜在重整,兰姆位移和平均力吉布斯态,移动还是不移动?","authors":"Luis A. Correa, Jonas Glatthard","doi":"10.22331/q-2025-09-30-1868","DOIUrl":null,"url":null,"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.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"19 1","pages":""},"PeriodicalIF":5.1000,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Potential renormalisation, Lamb shift and mean-force Gibbs state – to shift or not to shift?\",\"authors\":\"Luis A. Correa, Jonas Glatthard\",\"doi\":\"10.22331/q-2025-09-30-1868\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":20807,\"journal\":{\"name\":\"Quantum\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":5.1000,\"publicationDate\":\"2025-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.22331/q-2025-09-30-1868\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.22331/q-2025-09-30-1868","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Potential renormalisation, Lamb shift and mean-force Gibbs state – to shift or not to shift?
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.
QuantumPhysics 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.