Ground state energy of dilute Bose gases in 1D
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909379506208768 |
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| author | Agerskov, Johannes Reuvers, Robin Solovej, Jan Philip |
| author_facet | Agerskov, Johannes Reuvers, Robin Solovej, Jan Philip |
| contents | We study the ground state energy of a gas of 1D bosons with density $ρ$, interacting through a general, repulsive 2-body potential with scattering length $a$, in the dilute limit $ρ|a|\ll1$. The first terms in the expansion of the thermodynamic energy density are $π^2ρ^3/3(1+2ρa)$, where the leading order is the 1D free Fermi gas. This result covers the Tonks-Girardeau limit of the Lieb-Liniger model as a special case, but given the possibility that $a>0$, it also applies to potentials that differ significantly from a delta function. We include extensions to spinless fermions and 1D anyonic symmetries, and discuss an application to confined 3D gases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_17183 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ground state energy of dilute Bose gases in 1D Agerskov, Johannes Reuvers, Robin Solovej, Jan Philip Mathematical Physics Quantum Physics We study the ground state energy of a gas of 1D bosons with density $ρ$, interacting through a general, repulsive 2-body potential with scattering length $a$, in the dilute limit $ρ|a|\ll1$. The first terms in the expansion of the thermodynamic energy density are $π^2ρ^3/3(1+2ρa)$, where the leading order is the 1D free Fermi gas. This result covers the Tonks-Girardeau limit of the Lieb-Liniger model as a special case, but given the possibility that $a>0$, it also applies to potentials that differ significantly from a delta function. We include extensions to spinless fermions and 1D anyonic symmetries, and discuss an application to confined 3D gases. |
| title | Ground state energy of dilute Bose gases in 1D |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2203.17183 |