We consider a system of N bosons in a unitary box in the grand-canonical setting interacting through a potential with the scattering length scaling as N^{ −1+κ} , κ ∈ (0, 2/3). This regimes interpolate between the Gross–Pitaevskii regime (κ = 0) and the thermodynamic limit (κ = 2/3). In the work of Basti et al. [Forum Math., Sigma 9, E74 (2021)], as an intermediate step to prove an upper bound in agreement with the Lee–Huang–Yang formula in the thermodynamic limit, a second order upper bound on the ground state energy for κ < 5/9 was obtained. In this paper, thanks to a more careful analysis of the error terms, we extend the mentioned result to κ < 7/12.
A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime / Basti, Giulia. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 63:7(2022). [10.1063/5.0089790]
A second order upper bound on the ground state energy of a Bose gas beyond the Gross-Pitaevskii regime
Basti, Giulia
2022
Abstract
We consider a system of N bosons in a unitary box in the grand-canonical setting interacting through a potential with the scattering length scaling as N^{ −1+κ} , κ ∈ (0, 2/3). This regimes interpolate between the Gross–Pitaevskii regime (κ = 0) and the thermodynamic limit (κ = 2/3). In the work of Basti et al. [Forum Math., Sigma 9, E74 (2021)], as an intermediate step to prove an upper bound in agreement with the Lee–Huang–Yang formula in the thermodynamic limit, a second order upper bound on the ground state energy for κ < 5/9 was obtained. In this paper, thanks to a more careful analysis of the error terms, we extend the mentioned result to κ < 7/12.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
