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The Ground State Energy of a Two-Dimensional Bose Gas

Communications in Mathematical Physics, ISSN: 1432-0916, Vol: 405, Issue: 3, Page: 59
2024
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Article Description

We prove the following formula for the ground state energy density of a dilute Bose gas with density ρ in 2 dimensions in the thermodynamic limit (Formula presented.) as ρa→0. Here Y=|log(ρa)| and a is the scattering length of the two-body potential. This result in 2 dimensions corresponds to the famous Lee–Huang–Yang formula in 3 dimensions. The proof is valid for essentially all positive potentials with finite scattering length, in particular, it covers the crucial case of the hard core potential.

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