Exact Density Profiles of 1D Quantum Fluids in the Thomas-Fermi Limit: Geometric Hierarchy to the Tonks-Girardeau Gas
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912957224452096 |
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| author | Suyari, Hiroki |
| author_facet | Suyari, Hiroki |
| contents | We present a geometric framework for 1D quantum fluids across interaction regimes in the Thomas-Fermi limit. Based on the Linearization Principle via the $q$-logarithm, macroscopic density profiles form a discrete hierarchy: the ideal Bose gas ($q=1$), the mean-field Gross-Pitaevskii condensate ($q=-1$), and the strongly correlated Tonks-Girardeau gas ($q=-3$). We further derive a universal sound velocity scaling, $c \propto ρ^{(1-q)/4}$, valid in the interacting regimes ($q \le -1$). This establishes a non-perturbative link between static geometry and dynamical excitations in many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Density Profiles of 1D Quantum Fluids in the Thomas-Fermi Limit: Geometric Hierarchy to the Tonks-Girardeau Gas Suyari, Hiroki Quantum Gases Statistical Mechanics Mathematical Physics We present a geometric framework for 1D quantum fluids across interaction regimes in the Thomas-Fermi limit. Based on the Linearization Principle via the $q$-logarithm, macroscopic density profiles form a discrete hierarchy: the ideal Bose gas ($q=1$), the mean-field Gross-Pitaevskii condensate ($q=-1$), and the strongly correlated Tonks-Girardeau gas ($q=-3$). We further derive a universal sound velocity scaling, $c \propto ρ^{(1-q)/4}$, valid in the interacting regimes ($q \le -1$). This establishes a non-perturbative link between static geometry and dynamical excitations in many-body systems. |
| title | Exact Density Profiles of 1D Quantum Fluids in the Thomas-Fermi Limit: Geometric Hierarchy to the Tonks-Girardeau Gas |
| topic | Quantum Gases Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2603.01273 |