{"title":"用伪谱和有限差分方法研究三维玻色-爱因斯坦凝聚动力学","authors":"Paulsamy Muruganandam, S. Adhikari","doi":"10.1088/0953-4075/36/12/310","DOIUrl":null,"url":null,"abstract":"We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross–Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose–Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge–Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank–Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.","PeriodicalId":16799,"journal":{"name":"Journal of Physics B","volume":"463 1","pages":"2501-2513"},"PeriodicalIF":0.0000,"publicationDate":"2002-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"97","resultStr":"{\"title\":\"Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods\",\"authors\":\"Paulsamy Muruganandam, S. Adhikari\",\"doi\":\"10.1088/0953-4075/36/12/310\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross–Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose–Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge–Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank–Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.\",\"PeriodicalId\":16799,\"journal\":{\"name\":\"Journal of Physics B\",\"volume\":\"463 1\",\"pages\":\"2501-2513\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2002-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"97\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physics B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0953-4075/36/12/310\",\"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 B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0953-4075/36/12/310","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods
We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross–Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose–Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge–Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank–Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.