Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases

DOI10.1063/1.5094331zbMath1416.82015arXiv1903.01271OpenAlexW2919618604MaRDI QIDQ5223589

Mathieu Lewin, Nicolas Rougerie, Phan Thành Nam

Publication date: 18 July 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.01271

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Statistical thermodynamics (82B30)

Related Items (5)

A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation ⋮ A path-integral analysis of interacting Bose gases and loop gases ⋮ Mean-field limits for quantum systems and nonlinear Gibbs measures ⋮ Classical field theory limit of many-body quantum Gibbs states in 2D and 3D ⋮ Convergence rate towards the fractional Hartree equation with singular potentials in higher Sobolev trace norms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A theory of regularity structures
• Derivation of nonlinear Gibbs measures from many-body quantum mechanics
• Geometric methods for nonlinear many-body quantum systems
• The mathematics of the Bose gas and its condensation.
• Mean field limit for bosons and infinite dimensional phase-space analysis
• The classical limit of quantum partition functions
• Strong solutions to the stochastic quantization equations.
• Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions \({d \leqslant 3}\)
• Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
• Statistical mechanics of the nonlinear Schrödinger equation.
• One-and-a-half quantum de Finetti theorems
• Derivation of Hartree's theory for generic mean-field Bose systems
• The classical limit of quantum spin systems
• Examples of bosonic de Finetti states over finite dimensional Hilbert spaces
• Effective Evolution Equations from Quantum Dynamics
• Gibbs measures on Brownian currents
• Remarks on the Gibbs measures for nonlinear dispersive equations
• Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits
• Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics
• Introduction

This page was built for publication: Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases