Bogoliubov theory for many-body quantum systems
type: Item
instance of: scholarly article
title: Bogoliubov theory for many-body quantum systems
zbMATH Open document ID: 1496.35335
DOI: 10.4171/ECR/18-1/22
author: B. Schlein
publication date: 2021-12-03T00:00:00Z
review text: Summary: We review some recent applications of rigorous Bogoliubov theory. We show how Bogoliubov theory can be used to approximate quantum fluctuations, both in the analysis of the energy spectrum and in the study of the dynamics of many-body quantum systems. For the entire collection see [Zbl 1465.35005].
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81V70
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 7438904
zbMATH Keywords: many-body quantum mechanics
zbMATH Keywords: Bogoliubov theory
zbMATH Keywords: Bose-Einstein condensates
zbMATH Keywords: mean-field limit
zbMATH Keywords: Hartree-Fock theory
zbMATH Keywords: Fröhlich polaron
MaRDI profile type: Publication
cites work: Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime
cites work: Mean-field evolution of fermionic systems
cites work: Complete Bose-Einstein condensation in the Gross-Pitaevskii regime
cites work: Bogoliubov theory in the Gross-Pitaevskii limit
cites work: Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime
cites work: Quantum many-body fluctuations around nonlinear Schrödinger dynamics
cites work: Fluctuations of \(N\)-particle quantum dynamics around the nonlinear Schrödinger equation
cites work: Second-order corrections to mean field evolution for weakly interacting bosons in the case of three-body interactions
cites work: Excitation spectrum of interacting bosons in the mean-field infinite-volume limit
cites work: Asymptotics for the polaron
cites work: Persistence of the spectral gap for the Landau-Pekar equations
cites work: The energy of dilute Bose gases
cites work: Derivation of an effective evolution equation for a strongly coupled polaron
cites work: A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations
cites work: Dynamics of a strongly coupled polaron
cites work: Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron
cites work: Correlation Energy of an Electron Gas at High Density
cites work: The classical field limit of scattering theory for non-relativistic many- boson systems. II
cites work: The excitation spectrum for weakly interacting Bosons in a trap
cites work: On the dynamics of polarons in the strong-coupling limit
cites work: Pair excitations and the mean field approximation of interacting Bosons. I
cites work: Second-order corrections to mean field evolution of weakly interacting bosons. I
cites work: Another proof of BEC in the GP-limit
cites work: On the correlation energy of interacting fermionic systems in the mean-field regime
cites work: Exact evolution versus mean field with second-order correction for bosons interacting via short-range two-body potential.
cites work: Fluctuations around Hartree states in the mean-field regime
cites work: Bogoliubov Spectrum of Interacting Bose Gases
cites work: Exact ground state energy of the strong-coupling polaron
cites work: A note on the Fröhlich dynamics in the strong coupling limit
cites work: Bogoliubov corrections and trace norm convergence for the Hartree dynamics
cites work: Bogoliubov correction to the mean-field dynamics of interacting bosons
cites work: Ground states of large bosonic systems: the Gross-Pitaevskii limit revisited
cites work: The excitation spectrum for weakly interacting bosons
full work available at URL: https://doi.org/10.4171/ecr/18-1/22
OpenAlex ID: W3163169891
description: scientific article; zbMATH DE number 7438904