W. Tarnowski, Dariusz Chru'sci'nski, S. Denisov, K. Życzkowski
{"title":"服从详细平衡的随机Lindblad操作符","authors":"W. Tarnowski, Dariusz Chru'sci'nski, S. Denisov, K. Życzkowski","doi":"10.1142/S1230161223500075","DOIUrl":null,"url":null,"abstract":"We introduce different ensembles of random Lindblad operators [Formula: see text], which satisfy quantum detailed balance condition with respect to given stationary state [Formula: see text] of size [Formula: see text], and investigate their spectral properties. Such operators are known as ‘Davies generators’ and their eigenvalues are real; however, their spectral densities depend on [Formula: see text]. We propose different structured ensembles of random matrices, which allow us to tackle the problem analytically in the extreme cases of Davies generators corresponding to random [Formula: see text] with a nondegenerate spectrum or the maximally mixed stationary state, [Formula: see text]. Interestingly, in the latter case the density can be reasonably well approximated by integrating out the imaginary component of the spectral density characteristic to the ensemble of random unconstrained Lindblad operators. The case of asymptotic states with partially degenerated spectra is also addressed. Finally, we demonstrate that similar universal properties hold for the detailed balance-obeying Kolmogorov generators obtained by applying superdecoherence to an ensemble of random Davies generators. In this way we construct an ensemble of random classical generators with imposed detailed balance condition.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"13 1","pages":"2350007:1-2350007:32"},"PeriodicalIF":1.3000,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Random Lindblad Operators Obeying Detailed Balance\",\"authors\":\"W. Tarnowski, Dariusz Chru'sci'nski, S. Denisov, K. Życzkowski\",\"doi\":\"10.1142/S1230161223500075\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce different ensembles of random Lindblad operators [Formula: see text], which satisfy quantum detailed balance condition with respect to given stationary state [Formula: see text] of size [Formula: see text], and investigate their spectral properties. Such operators are known as ‘Davies generators’ and their eigenvalues are real; however, their spectral densities depend on [Formula: see text]. We propose different structured ensembles of random matrices, which allow us to tackle the problem analytically in the extreme cases of Davies generators corresponding to random [Formula: see text] with a nondegenerate spectrum or the maximally mixed stationary state, [Formula: see text]. Interestingly, in the latter case the density can be reasonably well approximated by integrating out the imaginary component of the spectral density characteristic to the ensemble of random unconstrained Lindblad operators. The case of asymptotic states with partially degenerated spectra is also addressed. Finally, we demonstrate that similar universal properties hold for the detailed balance-obeying Kolmogorov generators obtained by applying superdecoherence to an ensemble of random Davies generators. In this way we construct an ensemble of random classical generators with imposed detailed balance condition.\",\"PeriodicalId\":54681,\"journal\":{\"name\":\"Open Systems & Information Dynamics\",\"volume\":\"13 1\",\"pages\":\"2350007:1-2350007:32\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-04-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Open Systems & Information Dynamics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/S1230161223500075\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Systems & Information Dynamics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/S1230161223500075","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Random Lindblad Operators Obeying Detailed Balance
We introduce different ensembles of random Lindblad operators [Formula: see text], which satisfy quantum detailed balance condition with respect to given stationary state [Formula: see text] of size [Formula: see text], and investigate their spectral properties. Such operators are known as ‘Davies generators’ and their eigenvalues are real; however, their spectral densities depend on [Formula: see text]. We propose different structured ensembles of random matrices, which allow us to tackle the problem analytically in the extreme cases of Davies generators corresponding to random [Formula: see text] with a nondegenerate spectrum or the maximally mixed stationary state, [Formula: see text]. Interestingly, in the latter case the density can be reasonably well approximated by integrating out the imaginary component of the spectral density characteristic to the ensemble of random unconstrained Lindblad operators. The case of asymptotic states with partially degenerated spectra is also addressed. Finally, we demonstrate that similar universal properties hold for the detailed balance-obeying Kolmogorov generators obtained by applying superdecoherence to an ensemble of random Davies generators. In this way we construct an ensemble of random classical generators with imposed detailed balance condition.
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.