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- Title
The Ground State Energy of a Two-Dimensional Bose Gas.
- Authors
Fournais, Søren; Girardot, Theotime; Junge, Lukas; Morin, Leo; Olivieri, Marco
- Abstract
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 e 2D (ρ) = 4 π ρ 2 Y (1 - Y | log Y | + (2 Γ + 1 2 + log (π)) Y) + o (ρ 2 Y 2) , as ρ a 2 → 0 . Here Y = | log (ρ a 2) | - 1 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.
- Subjects
GROUND state energy; BOSE-Einstein gas; SCATTERING (Physics); ENERGY density
- Publication
Communications in Mathematical Physics, 2024, Vol 405, Issue 3, p1
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-023-04907-2