{"title":"涉及雅可比函数的积分及其在量子系统中的应用","authors":"Emerson B. S. Corrêa, Carlos A Bahia","doi":"10.47363/jpsos/2023(5)206","DOIUrl":null,"url":null,"abstract":"We study four expressions involving the integrals of Jacobi’s theta functions. From Poisson’s summation formula, we write the integrals of the functions θi, (i = 1,2,3,4) in terms of modified Bessel functions of the second kind. For the integrals of θ1 , θ2 and θ3, we get expressions with real arguments, but for the integral of θ4 , we find an expression with imaginary argument. In addition, we apply our results to the description of two kinds of interacting quantum systems: boson gas and fermion gas both under a thermal bath and an external magnetic field. PACS numbers:","PeriodicalId":476909,"journal":{"name":"Journal of Physics & Optics Sciences","volume":"11 3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integrals Involving Jacobi Theta Functions and Applications in Quantum Systems\",\"authors\":\"Emerson B. S. Corrêa, Carlos A Bahia\",\"doi\":\"10.47363/jpsos/2023(5)206\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study four expressions involving the integrals of Jacobi’s theta functions. From Poisson’s summation formula, we write the integrals of the functions θi, (i = 1,2,3,4) in terms of modified Bessel functions of the second kind. For the integrals of θ1 , θ2 and θ3, we get expressions with real arguments, but for the integral of θ4 , we find an expression with imaginary argument. In addition, we apply our results to the description of two kinds of interacting quantum systems: boson gas and fermion gas both under a thermal bath and an external magnetic field. PACS numbers:\",\"PeriodicalId\":476909,\"journal\":{\"name\":\"Journal of Physics & Optics Sciences\",\"volume\":\"11 3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physics & Optics Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47363/jpsos/2023(5)206\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics & Optics Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47363/jpsos/2023(5)206","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了涉及雅可比函数积分的四种表达式。从泊松求和公式出发，用第二类修正贝塞尔函数表示函数θi， (i = 1,2,3,4)的积分。对于θ1， θ2和θ3的积分，我们得到了实参数的表达式，但是对于θ4的积分，我们找到了虚参数的表达式。此外，我们将我们的结果应用于两种相互作用量子系统的描述:在热浴和外磁场下的玻色子气体和费米子气体。pac数字:
Integrals Involving Jacobi Theta Functions and Applications in Quantum Systems
We study four expressions involving the integrals of Jacobi’s theta functions. From Poisson’s summation formula, we write the integrals of the functions θi, (i = 1,2,3,4) in terms of modified Bessel functions of the second kind. For the integrals of θ1 , θ2 and θ3, we get expressions with real arguments, but for the integral of θ4 , we find an expression with imaginary argument. In addition, we apply our results to the description of two kinds of interacting quantum systems: boson gas and fermion gas both under a thermal bath and an external magnetic field. PACS numbers:
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