Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit
arXiv:2305.19173 · doi:10.1137/23M1580930
Abstract
We consider a homogeneous Bose gas in the Gross-Pitaevskii limit at temperatures that are comparable to the critical temperature for Bose-Einstein condensation in the ideal gas. Our main result is an upper bound for the grand canonical free energy in terms of two new contributions: (a) the free energy of the interacting condensate is given in terms of an effective theory describing its particle number fluctuations, (b) the free energy of the thermally excited particles equals that of a temperature-dependent Bogoliubov Hamiltonian.
41 pages
References in corpus (12)
- The Second Order Upper Bound for the Ground Energy of a Bose Gas
- Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
- Interaction Effects on Number Fluctuations in a Bose-Einstein Condensate of Light
- Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
- Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
- The Mathematics of the Bose Gas and its Condensation
- Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
- Another proof of BEC in the GP-limit
- A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
- The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime
- The Bose gas in a box with Neumann boundary conditions
- The free energy of the two-dimensional dilute Bose gas. II. Upper bound
Cited by in corpus (5)
- Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation
- Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit for general interaction potentials
- Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
- The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
- Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime