Asymptotic analysis of the weakly interacting Bose gas: A collection of recent results and applications
arXiv:2304.12910 · doi:10.1007/978-3-031-45434-9_22
Abstract
We consider a gas of N bosons with interactions in the mean-field scaling regime. We review a recent proof of the asymptotic expansion of its spectrum and eigenstates and two applications of this result, namely the derivation of an Edgeworth expansion for fluctuations of one-body operators and the computation of the binding energy of an inhomogeneous Bose gas to any order. Finally, we collect related results for the dynamics of the weakly interacting Bose gas and for the regularized Nelson model.
arXiv comment12 pages
References in corpus (24)
- Mean-Field Dynamics: Singular Potentials and Rate of Convergence
- On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
- Second-order corrections to mean field evolution for weakly interacting Bosons. I
- The excitation spectrum for weakly interacting bosons in a trap
- The Excitation Spectrum for Weakly Interacting Bosons
- Rate of Convergence Towards Hartree Dynamics
- Second-order corrections to mean-field evolution of weakly interacting Bosons, II
- Bogoliubov corrections and trace norm convergence for the Hartree dynamics
- On the rate of convergence for the mean field approximation of many-body quantum dynamics
- Asymptotic expansion of low-energy excitations for weakly interacting bosons
- Bogoliubov correction to the mean-field dynamics of interacting bosons
- Mean field limit for bosons and propagation of Wigner measures
- Classical limit of the Nelson model with cut off
- Higher order corrections to the mean-field description of the dynamics of interacting bosons
- Beyond Bogoliubov Dynamics
- Edgeworth expansions for weakly dependent random variables
- Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy
- Central limit theorem for Bose gases interacting through singular potentials
- A large deviation principle in many-body quantum dynamics
- Mean-field limits of particles in interaction with quantized radiation fields
- Large deviation estimates for weakly interacting bosons
- Binding energy of homogeneous Bose gas
- Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
- Weak Edgeworth expansion for the mean-field interacting Bose gas