{"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}
引用次数: 0
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:
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:
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