{"title":"On the factorization method for the quantum statistical description of dynamics of an isolated spin system","authors":"A. A. Samokhin, A. V. Zyl, N. L. Zamarashkin","doi":"10.1134/S0040577924030061","DOIUrl":null,"url":null,"abstract":"<p> We study the applicability of the formula that factors the trace of the diagonal part of spin operator products in the case of a relatively small number of particles of an isolated spin system. The validity of this formula for a large number of particles follows from the basic principles of quantum statistical mechanics. The spin system under consideration includes dipole–dipole interaction and the Zeeman interaction with an external magnetic field. We establish that the accuracy of this formula monotonically increases as the magnetic field increases. At the same time, the dependence on the number of particles in the range <span>\\(2\\div10\\)</span> for various configurations turns out to be sharply nonmonotone. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577924030061","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}
引用次数: 0
Abstract
We study the applicability of the formula that factors the trace of the diagonal part of spin operator products in the case of a relatively small number of particles of an isolated spin system. The validity of this formula for a large number of particles follows from the basic principles of quantum statistical mechanics. The spin system under consideration includes dipole–dipole interaction and the Zeeman interaction with an external magnetic field. We establish that the accuracy of this formula monotonically increases as the magnetic field increases. At the same time, the dependence on the number of particles in the range \(2\div10\) for various configurations turns out to be sharply nonmonotone.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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