{"title":"时变Gross-Pitaevskii方程的数值解","authors":"Tsogbayar Tsednee, B. Tsednee, Tsookhuu Khinayat","doi":"10.5564/jasea.v3i1.2456","DOIUrl":null,"url":null,"abstract":"In this work we employ the split-step technique combined with a Legendre pseudospectral representation to solve various time-dependent GrossPitaevskii equations (GPE). Our findings based on the numerical accuracy of this approach applied for one-dimensional (1D) and two-dimensional (2D) problems show that it can provide accurate and stable solutions. Moreover, this approach has been applied to study the dynamics of the Bose-Einstein condensate which is modeled with the GPE. The breathing of condensate with a repulsive and attractive interactions trapped in 1D and 2D harmonic potentials has been simulated as well.","PeriodicalId":7757,"journal":{"name":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Numerical solution to the time-dependent Gross-Pitaevskii equation\",\"authors\":\"Tsogbayar Tsednee, B. Tsednee, Tsookhuu Khinayat\",\"doi\":\"10.5564/jasea.v3i1.2456\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work we employ the split-step technique combined with a Legendre pseudospectral representation to solve various time-dependent GrossPitaevskii equations (GPE). Our findings based on the numerical accuracy of this approach applied for one-dimensional (1D) and two-dimensional (2D) problems show that it can provide accurate and stable solutions. Moreover, this approach has been applied to study the dynamics of the Bose-Einstein condensate which is modeled with the GPE. The breathing of condensate with a repulsive and attractive interactions trapped in 1D and 2D harmonic potentials has been simulated as well.\",\"PeriodicalId\":7757,\"journal\":{\"name\":\"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering\",\"volume\":\"32 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5564/jasea.v3i1.2456\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Anadolu University Journal of Science and Technology-A Applied Sciences and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5564/jasea.v3i1.2456","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Numerical solution to the time-dependent Gross-Pitaevskii equation
In this work we employ the split-step technique combined with a Legendre pseudospectral representation to solve various time-dependent GrossPitaevskii equations (GPE). Our findings based on the numerical accuracy of this approach applied for one-dimensional (1D) and two-dimensional (2D) problems show that it can provide accurate and stable solutions. Moreover, this approach has been applied to study the dynamics of the Bose-Einstein condensate which is modeled with the GPE. The breathing of condensate with a repulsive and attractive interactions trapped in 1D and 2D harmonic potentials has been simulated as well.
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