Ground State and Collective Modes of Bose-Einstein Condensates in Newtonian and MOND-inspired gravitational potentials
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912801455341568 |
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| author | Liu, Ning |
| author_facet | Liu, Ning |
| contents | We analytically and numerically study the ground state and collective dynamics of Bose-Einstein condensates in two traps: a Newtonian potential and a logarithmic potential inspired by Modified Newtonian Dynamics (MOND). In the ground state, the MOND potential supports bound states only in the deep-MOND regime, where the condensate becomes significantly larger than its Newtonian counterpart. The size increases with repulsive coupling parameter $β$ in both potentials. A clear scaling law of the size with $β^{1/3}$ emerges in the MOND case and is confirmed numerically over a wide parameter range, while for the Newtonian potential no simple scaling law exists as the Thomas-Fermi approximation ceases to be valid. For the dynamics, we derive and solve equations for the monopole collective mode. The larger MOND-bound condensate oscillates at a lower frequency, which scales as $β^{-1/3}$ in the strong-interaction limit. These scaling laws provide insights for quantum-simulation experiments aiming to probe modified-gravity scenarios with cold atoms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01039 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground State and Collective Modes of Bose-Einstein Condensates in Newtonian and MOND-inspired gravitational potentials Liu, Ning Quantum Gases Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies General Relativity and Quantum Cosmology Quantum Physics We analytically and numerically study the ground state and collective dynamics of Bose-Einstein condensates in two traps: a Newtonian potential and a logarithmic potential inspired by Modified Newtonian Dynamics (MOND). In the ground state, the MOND potential supports bound states only in the deep-MOND regime, where the condensate becomes significantly larger than its Newtonian counterpart. The size increases with repulsive coupling parameter $β$ in both potentials. A clear scaling law of the size with $β^{1/3}$ emerges in the MOND case and is confirmed numerically over a wide parameter range, while for the Newtonian potential no simple scaling law exists as the Thomas-Fermi approximation ceases to be valid. For the dynamics, we derive and solve equations for the monopole collective mode. The larger MOND-bound condensate oscillates at a lower frequency, which scales as $β^{-1/3}$ in the strong-interaction limit. These scaling laws provide insights for quantum-simulation experiments aiming to probe modified-gravity scenarios with cold atoms. |
| title | Ground State and Collective Modes of Bose-Einstein Condensates in Newtonian and MOND-inspired gravitational potentials |
| topic | Quantum Gases Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2601.01039 |