{"title":"反平方势中玻色子凝聚体中的角动量模式","authors":"Hidetsugu Sakaguchi, Boris A. Malomed","doi":"10.3390/sym15112060","DOIUrl":null,"url":null,"abstract":"In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r)=−U0/2r2 is suppressed by repulsive inter-particle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying angular momentum, with the orbital and magnetic quantum numbers l and m. They exist above a threshold value of the potential’s strength, U0>l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m=l, 0<m<l, and m=0, respectively, are found in an approximate analytical form for relatively small values of U0−l(l+1). Explicit results are produced for the p- and d-wave states, with l=1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"37 1","pages":"0"},"PeriodicalIF":2.2000,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Angular-Momentum Modes in a Bosonic Condensate Trapped in the Inverse-Square Potential\",\"authors\":\"Hidetsugu Sakaguchi, Boris A. Malomed\",\"doi\":\"10.3390/sym15112060\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r)=−U0/2r2 is suppressed by repulsive inter-particle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying angular momentum, with the orbital and magnetic quantum numbers l and m. They exist above a threshold value of the potential’s strength, U0>l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m=l, 0<m<l, and m=0, respectively, are found in an approximate analytical form for relatively small values of U0−l(l+1). Explicit results are produced for the p- and d-wave states, with l=1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.\",\"PeriodicalId\":48874,\"journal\":{\"name\":\"Symmetry-Basel\",\"volume\":\"37 1\",\"pages\":\"0\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry-Basel\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/sym15112060\",\"RegionNum\":3,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry-Basel","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym15112060","RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Angular-Momentum Modes in a Bosonic Condensate Trapped in the Inverse-Square Potential
In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r)=−U0/2r2 is suppressed by repulsive inter-particle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying angular momentum, with the orbital and magnetic quantum numbers l and m. They exist above a threshold value of the potential’s strength, U0>l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m=l, 0
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Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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