The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime

Abstract

Bogoliubov Theory provides important predictions for the low energy properties of the weakly interacting Bose gas. Recently, Bogoliubov's predictions could be justified rigorously in \cite{BBCS3} for translation invariant systems in the Gross-Pitaveskii regime, where $N$ bosons in $\Lambda =[0;1{]}^3\subset {\mathbb{R}}^3$ interact through a potential whose scattering length is of size $N^{-1}$. In this note, we review recent results from \cite{BSS2}, a joint work with B. Schlein and S. Schraven, which extends the analysis of \cite{BBCS3} to systems of bosons in ${\mathbb{R}}^3$ that are trapped by an external potential.

arXiv commentContribution to the Proceedings of ICMP 2021, 17 pages

References in corpus (24)

• Proof of Bose-Einstein Condensation for Dilute Trapped Gases
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases
• The excitation spectrum for weakly interacting bosons in a trap
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The Excitation Spectrum for Weakly Interacting Bosons
• Quantitative Derivation of the Gross-Pitaevskii Equation
• The ground state energy of a low density Bose gas: a second order upper bound
• Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime
• Ground states of large bosonic systems: The gross-pitaevskii limit revisited
• Gross-Pitaevskii Dynamics for Bose-Einstein Condensates
• Excitation spectrum of interacting bosons in the mean-field infinite-volume limit
• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime
• Asymptotic expansion of low-energy excitations for weakly interacting bosons
• Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
• The Bogoliubov free energy functional II. The dilute limit
• The Bogoliubov free energy functional I. Existence of minimizers and phase diagram
• Another proof of BEC in the GP-limit
• A simple 2nd order lower bound to the energy of dilute Bose gases
• Bose particles in a box III. A convergent expansion of the ground state of the Hamiltonian in the mean field limiting regime
• On Bose-Einstein condensates in the Thomas-Fermi regime
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger

Cited by in corpus (1)

• Reduced fluctuations for bosons in a double well