Validity of Bogoliubov’s approximation for translation-invariant Bose gases

We verify Bogoliubov’s approximation for translation-invariant Bose gases in the mean field regime, i.e., we prove that the ground state energy $E_{N}$ is given by $E_{N} = N e_{H} + inf σ (ℍ) + o_{N \to \infty} (1)$ , where $N$ is the number of particles, $e_{H}$ is the minimal Hartree energy and $ℍ$ is the Bogoliubov Hamiltonian. As an intermediate result we show the existence of approximate ground states $Ψ_{N}$ , i.e., states satisfying ${⟨ H_{N} ⟩}_{Ψ_{N}} = E_{N} + o_{N \to \infty} (1)$ , exhibiting complete Bose–Einstein condensation with respect to one of the Hartree minimizers.

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Keywords

Bose gas, translation-invariant, Bogoliubov approximation, Bose–Einstein condensation

Mathematical Subject Classification

Primary: 81V70

Milestones

Received: 2 February 2022

Revised: 20 July 2022

Accepted: 9 August 2022

Published: 21 February 2023

Authors

Morris Brooks
Institute of Science and Technology Austria Klosterneuburg Austria

Robert Seiringer
Institute of Science and Technology Austria Klosterneuburg Austria

Vol. 3, No. 4, 2022

Morris Brooks and Robert Seiringer

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors