{"title":"点物质黑洞和非交换黑洞模型中的哈密顿映射和量子扰动方程","authors":"Jun Yan","doi":"10.1134/S0040577924110138","DOIUrl":null,"url":null,"abstract":"<p> The Hamiltonian mapping of the Dirac equation with a quantum perturbation in <span>\\(2\\)</span>D black hole models are investigated. We derive the Hamiltonians of the modified Rabi model for the point matter black hole and noncommutative black hole, and obtain perturbed expressions for the velocity and acceleration of the simulating Dirac particles. The fluctuation equations for the charge–current density in two types of black holes are derived based on the solutions of the Dirac equation. The results indicate that the Hamiltonians contain the correction terms with different powers of the creation and annihilation operators, and the accelerations have some additional Dirac Zitterbewegung terms. In addition, the coordinate operators in the fluctuation equations of the charge–current density have different powers. These characteristics can be used to distinguish different types of black holes in the analogical gravity models. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":"221 2","pages":"1994 - 2006"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hamiltonian mapping and quantum perturbation equations in the point matter black hole and noncommutative black hole models\",\"authors\":\"Jun Yan\",\"doi\":\"10.1134/S0040577924110138\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The Hamiltonian mapping of the Dirac equation with a quantum perturbation in <span>\\\\(2\\\\)</span>D black hole models are investigated. We derive the Hamiltonians of the modified Rabi model for the point matter black hole and noncommutative black hole, and obtain perturbed expressions for the velocity and acceleration of the simulating Dirac particles. The fluctuation equations for the charge–current density in two types of black holes are derived based on the solutions of the Dirac equation. The results indicate that the Hamiltonians contain the correction terms with different powers of the creation and annihilation operators, and the accelerations have some additional Dirac Zitterbewegung terms. In addition, the coordinate operators in the fluctuation equations of the charge–current density have different powers. These characteristics can be used to distinguish different types of black holes in the analogical gravity models. </p>\",\"PeriodicalId\":797,\"journal\":{\"name\":\"Theoretical and Mathematical Physics\",\"volume\":\"221 2\",\"pages\":\"1994 - 2006\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-11-26\",\"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/S0040577924110138\",\"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":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S0040577924110138","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}
Hamiltonian mapping and quantum perturbation equations in the point matter black hole and noncommutative black hole models
The Hamiltonian mapping of the Dirac equation with a quantum perturbation in \(2\)D black hole models are investigated. We derive the Hamiltonians of the modified Rabi model for the point matter black hole and noncommutative black hole, and obtain perturbed expressions for the velocity and acceleration of the simulating Dirac particles. The fluctuation equations for the charge–current density in two types of black holes are derived based on the solutions of the Dirac equation. The results indicate that the Hamiltonians contain the correction terms with different powers of the creation and annihilation operators, and the accelerations have some additional Dirac Zitterbewegung terms. In addition, the coordinate operators in the fluctuation equations of the charge–current density have different powers. These characteristics can be used to distinguish different types of black holes in the analogical gravity models.
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.