{"title":"Quantum Random Evolutions","authors":"Henryk Gzyl","doi":"10.1007/s10955-024-03284-x","DOIUrl":null,"url":null,"abstract":"<p>In this work, we develop a mathematical framework to model a quantum system whose time evolution may depend on the state of a randomly changing environment that evolves according to a Markovian process. When the environment changes its state, three possible things may occur: the quantum system starts evolving according to a new Hamiltonian, it may suffer an instantaneous perturbation that changes its state or both things may happen simultaneously. We consider the case of quantum systems with finite dimensional Hilbert state space, in which case the observables are described by Hermitian matrices. We show how to average over the environment to predict the expected value of the density matrix with which one can compute the expected values of the observables of interest.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10955-024-03284-x","RegionNum":3,"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}
引用次数: 0
Abstract
In this work, we develop a mathematical framework to model a quantum system whose time evolution may depend on the state of a randomly changing environment that evolves according to a Markovian process. When the environment changes its state, three possible things may occur: the quantum system starts evolving according to a new Hamiltonian, it may suffer an instantaneous perturbation that changes its state or both things may happen simultaneously. We consider the case of quantum systems with finite dimensional Hilbert state space, in which case the observables are described by Hermitian matrices. We show how to average over the environment to predict the expected value of the density matrix with which one can compute the expected values of the observables of interest.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.