Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2
We investigate the ground states of 3-component Bose–Einstein condensates with harmonic-like trapping potentials in ℝ2{\mathbb{R}^{2}}, where the intra-component interactions μi{\mu_{i}} and the inter-component interactions βij=βji{\beta_{ij}=\beta_{ji}} (i,j=1,2,3{i,j=1,2,3}, i≠j{i\neq j}) are al...
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-08-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2021-2131 |
| _version_ | 1811280149467889664 |
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| author | Kong Yuzhen Wang Qingxuan Zhao Dun |
| author_facet | Kong Yuzhen Wang Qingxuan Zhao Dun |
| author_sort | Kong Yuzhen |
| collection | DOAJ |
| description | We investigate the ground states of 3-component Bose–Einstein condensates with harmonic-like trapping potentials in ℝ2{\mathbb{R}^{2}}, where the intra-component interactions μi{\mu_{i}} and the inter-component interactions βij=βji{\beta_{ij}=\beta_{ji}} (i,j=1,2,3{i,j=1,2,3}, i≠j{i\neq j}) are all attractive. We display the regions of μi{\mu_{i}} and βij{\beta_{ij}} for the existence and nonexistence of the ground states, and give an elaborate analysis for the asymptotic behavior of the ground states as βij↗βij*:=a∗+12(a∗-μi)(a∗-μj){\beta_{ij}\nearrow\beta_{ij}^{*}:=a^{\ast}+\frac{1}{2}\sqrt{{(a^{\ast}-\mu_{i% })(a^{\ast}-\mu_{j})}}}, where 0<μi<a∗:=∥w∥22{0<\mu_{i}<a^{\ast}:=\|w\|_{2}^{2}} are fixed and w is the unique positive solution of Δw-w+w3=0{\Delta w-w+w^{3}=0} in H1(ℝ2){H^{1}(\mathbb{R}^{2})}. The energy estimation as well as the mass concentration phenomena are studied, and when two of the intra-component interactions are equal, the nondegeneracy and the uniqueness of the ground states are proved. |
| first_indexed | 2024-04-13T01:08:20Z |
| format | Article |
| id | doaj.art-fe183edfe25341ca91e334bc7d00a682 |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-13T01:08:20Z |
| publishDate | 2021-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-fe183edfe25341ca91e334bc7d00a6822022-12-22T03:09:16ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752021-08-0121359363210.1515/ans-2021-2131Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2Kong Yuzhen0Wang Qingxuan1Zhao Dun2School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. ChinaWe investigate the ground states of 3-component Bose–Einstein condensates with harmonic-like trapping potentials in ℝ2{\mathbb{R}^{2}}, where the intra-component interactions μi{\mu_{i}} and the inter-component interactions βij=βji{\beta_{ij}=\beta_{ji}} (i,j=1,2,3{i,j=1,2,3}, i≠j{i\neq j}) are all attractive. We display the regions of μi{\mu_{i}} and βij{\beta_{ij}} for the existence and nonexistence of the ground states, and give an elaborate analysis for the asymptotic behavior of the ground states as βij↗βij*:=a∗+12(a∗-μi)(a∗-μj){\beta_{ij}\nearrow\beta_{ij}^{*}:=a^{\ast}+\frac{1}{2}\sqrt{{(a^{\ast}-\mu_{i% })(a^{\ast}-\mu_{j})}}}, where 0<μi<a∗:=∥w∥22{0<\mu_{i}<a^{\ast}:=\|w\|_{2}^{2}} are fixed and w is the unique positive solution of Δw-w+w3=0{\Delta w-w+w^{3}=0} in H1(ℝ2){H^{1}(\mathbb{R}^{2})}. The energy estimation as well as the mass concentration phenomena are studied, and when two of the intra-component interactions are equal, the nondegeneracy and the uniqueness of the ground states are proved.https://doi.org/10.1515/ans-2021-2131ground state3-component bose–einstein condensatemass concentrationnondegeneracyuniqueness35j50 35q40 35q55 |
| spellingShingle | Kong Yuzhen Wang Qingxuan Zhao Dun Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2 Advanced Nonlinear Studies ground state 3-component bose–einstein condensate mass concentration nondegeneracy uniqueness 35j50 35q40 35q55 |
| title | Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2 |
| title_full | Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2 |
| title_fullStr | Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2 |
| title_full_unstemmed | Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2 |
| title_short | Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2 |
| title_sort | mass concentration and asymptotic uniqueness of ground state for 3 component bec with external potential in r2 |
| topic | ground state 3-component bose–einstein condensate mass concentration nondegeneracy uniqueness 35j50 35q40 35q55 |
| url | https://doi.org/10.1515/ans-2021-2131 |
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