# Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons

@article{Deuchert2020SemiclassicalAA,
title={Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons},
author={Andreas Deuchert and Robert Seiringer},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 2 September 2020
• Physics
• arXiv: Mathematical Physics
1 Citations
• Physics
• 2022
We study the time-evolution of an initially trapped weakly interacting Bose gas at positive temperature, after the trapping potential has been switched off. It has been recently shown in [24] that

## References

SHOWING 1-10 OF 90 REFERENCES

• Mathematics
• 1976
We extend the Prekopa-Leindler theorem to other types of convex combinations of two positive functions and we strengthen the Prekopa—Leindler and Brunn-Minkowski theorems by introducing the notion of
• Mathematics, Physics
• 2007
We derive rigorously the one-dimensional cubic nonlinear Schrödinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weak-coupling limit together with a
• Materials Science
Communications in Mathematical Physics
• 2017
We prove that Gibbs measures of nonlinear Schrödinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing interactions in
• Physics
Annales Henri Poincaré
• 2021
A new derivation of this formula for the ground state energy at second order in the particle density is given, inspired by Bogoliubov theory, and it makes use of the almost-bosonic nature of the low-energy excitations of the systems.
• Physics
• 2020
We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the
• Mathematics, Physics
Journal of Mathematical Physics
• 2020
We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for $a^2 \rho \ll 1$ and $\beta \rho \gtrsim 1$ the free energy per unit
• Mathematics
• 2020
We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schr\"odinger equation in the mean-field limit, where the density of the
• Mathematics
Forum of Mathematics, Sigma
• 2020
We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\unicode[STIX]{x1D70C}$ and inverse
Introduction The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography.