Mean-field limit of Bose systems: rigorous results

Abstract

We review recent results about the derivation of the Gross-Pitaevskii equation and of the Bogoliubov excitation spectrum, starting from many-body quantum mechanics. We focus on the mean-field regime, where the interaction is multiplied by a coupling constant of order 1/N where N is the number of particles in the system.

Proceedings from the International Congress of Mathematical Physics at Santiago de Chile, July 2015

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Cited by in corpus (16)

• Derivation of the Time Dependent Two Dimensional Focusing NLS Equation
• Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
• Some contributions to many-body quantum mathematics
• The rigorous derivation of the ${\mathbb{T}}^2$ focusing cubic NLS from 3D
• Tosio Kato's Work on Non--Relativistic Quantum Mechanics
• Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
• Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases
• Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
• Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics
• Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons
• Bose Gases at Positive Temperature and Non-Linear Gibbs Measures
• Uniform in $N$ Global Well-posedness of the Time-Dependent Hartree-Fock-Bogoliubov Equations in ${\mathbb{R}}^{1+1}$
• Proper condensates and off-diagonal long range order
• Limites de champ moyen bosoniques {à} temp{é}rature positive
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
• Differential Equations of Quantum Mechanics