A second order upper bound to the free energy of the two dimensional Bose gas
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913024173932544 |
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| author | Haberberger, Florian Junge, Lukas |
| author_facet | Haberberger, Florian Junge, Lukas |
| contents | We consider a two-dimensional Bose gas in the dilute regime where $ρa^2$ is small. For temperatures below the Berezinskii-Kosterlitz-Thouless critical temperature, we derive an explicit upper bound for the free energy density using Bogoliubov theory. Our result captures the contribution of quasiparticle modes with dispersion relation $\sqrt{p^4 + 8πρ\, δ\, p^2}$ and where $δ= 2 / (|\log(ρa^2)| + \log |\log(ρa^2)|)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_10270 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A second order upper bound to the free energy of the two dimensional Bose gas Haberberger, Florian Junge, Lukas Mathematical Physics We consider a two-dimensional Bose gas in the dilute regime where $ρa^2$ is small. For temperatures below the Berezinskii-Kosterlitz-Thouless critical temperature, we derive an explicit upper bound for the free energy density using Bogoliubov theory. Our result captures the contribution of quasiparticle modes with dispersion relation $\sqrt{p^4 + 8πρ\, δ\, p^2}$ and where $δ= 2 / (|\log(ρa^2)| + \log |\log(ρa^2)|)$. |
| title | A second order upper bound to the free energy of the two dimensional Bose gas |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2604.10270 |