Bogoliubov theory for trapped bosons in the Gross-Pitaevskii regime

DOI10.1007/s00023-021-01151-zzbMath1489.82046arXiv2108.11129OpenAlexW3195886383MaRDI QIDQ2135175

Benjamin Schlein, Severin Schraven, Christian Brennecke

Publication date: 4 May 2022

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.11129

zbMATH Keywords

Gross-Pitaevskii equationBogoliubov theorysystems of \(N\) bosons

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Bosonic systems in quantum theory (81V73)

Related Items (15)

The low energy spectrum of trapped bosons in the Gross–Pitaevskii regime ⋮ Dilute Bose gas with three-body interaction: Recent results and open questions ⋮ Ground state energy of a Bose gas in the Gross–Pitaevskii regime ⋮ Reduced fluctuations for bosons in a double well ⋮ Bogoliubov theory in the Gross-Pitaevskii limit: a simplified approach ⋮ The Bose gas in a box with Neumann boundary conditions ⋮ On the characterisation of fragmented Bose–Einstein condensation and its emergent effective evolution ⋮ Bogoliubov excitation spectrum of Bose gases ⋮ Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime ⋮ Beyond mean-field: Condensate coupled with pair excitations ⋮ An optimal upper bound for the dilute Fermi gas in three dimensions ⋮ Exponential decay of the number of excitations in the weakly interacting Bose gas ⋮ Validity of Bogoliubov's approximation for translation-invariant Bose gases ⋮ A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime ⋮ On Bose-Einstein condensates in the Thomas-Fermi regime

Cites Work

• Ground states of large bosonic systems: the Gross-Pitaevskii limit revisited
• The excitation spectrum for weakly interacting Bosons in a trap
• Excitation spectrum of interacting bosons in the mean-field infinite-volume limit
• The excitation spectrum for weakly interacting bosons
• The excitation spectrum of Bose gases interacting through singular potentials
• The second order upper bound for the ground energy of a Bose gas
• Derivation of the Gross-Pitaevskii equation for rotating Bose gases
• Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
• Bogoliubov theory in the Gross-Pitaevskii limit
• A simple 2nd order lower bound to the energy of dilute Bose gases
• Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime
• The energy of dilute Bose gases
• Gross-Pitaevskii dynamics for Bose-Einstein condensates
• Bose-Einstein condensation beyond the Gross-Pitaevskii regime
• Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate
• Another proof of BEC in the GP-limit
• Bogoliubov Spectrum of Interacting Bose Gases
• Quantitative Derivation of the Gross‐Pitaevskii Equation
• Asymptotic expansion of low-energy excitations for weakly interacting bosons

This page was built for publication: Bogoliubov theory for trapped bosons in the Gross-Pitaevskii regime