{"title":"玻色-爱因斯坦凝聚中规则涡旋多边形的稳定性","authors":"A. Kilin, E. Artemova","doi":"10.35634/2226-3594-2020-56-02","DOIUrl":null,"url":null,"abstract":"We consider the problem of the stability of rotating regular vortex N-gons (Thomson configurations) in a Bose-Einstein condensate in a harmonic trap. The dependence of the rotation velocity ω of the Thomson configuration around the center of the trap is obtained as a function of the number of vortices N and the radius of the configuration R. The analysis of the stability of motion of such configurations in the linear approximation is carried out. For N⩽6, regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex N-gons for N > 6 are unstable for any parameters of the system.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"124 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Stability of regular vortex polygons in Bose-Einstein condensate\",\"authors\":\"A. Kilin, E. Artemova\",\"doi\":\"10.35634/2226-3594-2020-56-02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of the stability of rotating regular vortex N-gons (Thomson configurations) in a Bose-Einstein condensate in a harmonic trap. The dependence of the rotation velocity ω of the Thomson configuration around the center of the trap is obtained as a function of the number of vortices N and the radius of the configuration R. The analysis of the stability of motion of such configurations in the linear approximation is carried out. For N⩽6, regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex N-gons for N > 6 are unstable for any parameters of the system.\",\"PeriodicalId\":42053,\"journal\":{\"name\":\"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta\",\"volume\":\"124 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35634/2226-3594-2020-56-02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35634/2226-3594-2020-56-02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Stability of regular vortex polygons in Bose-Einstein condensate
We consider the problem of the stability of rotating regular vortex N-gons (Thomson configurations) in a Bose-Einstein condensate in a harmonic trap. The dependence of the rotation velocity ω of the Thomson configuration around the center of the trap is obtained as a function of the number of vortices N and the radius of the configuration R. The analysis of the stability of motion of such configurations in the linear approximation is carried out. For N⩽6, regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex N-gons for N > 6 are unstable for any parameters of the system.
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