Mean-field limits for quantum systems and nonlinear Gibbs measures

DOI10.4171/icm2022/53OpenAlexW4389775303MaRDI QIDQ6200705

Mathieu Lewin

Publication date: 24 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/icm2022/53

zbMATH Keywords

Bose-Einstein condensatesmean-field limitsnonlinear Gibbs measuresquantum de Finetti theorem

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) PDEs with randomness, stochastic partial differential equations (35R60) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Bosonic systems in quantum theory (81V73)

Cites Work

• Unnamed Item
• Unnamed Item
• GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions
• The excitation spectrum for weakly interacting Bosons in a trap
• 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.
• The excitation spectrum for weakly interacting bosons
• Classical theory of boson wave fields
• The excitation spectrum of Bose gases interacting through singular potentials
• The ground state energy of the weakly interacting Bose gas at high density
• Derivation of the Gross-Pitaevskii equation for rotating Bose gases
• Mean field limit for bosons and infinite dimensional phase-space analysis
• The Chandrasekhar theory of stellar collapse as the limit quantum mechanics
• Periodic nonlinear Schrödinger equation and invariant measures
• Invariant measures for the Gross-Pitaevskii equation
• Gibbs measures of nonlinear Schrödinger equations as limits of many-body quantum states in dimensions \({d \leqslant 3}\)
• The large deviation principle and some models of an interacting boson gas
• Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature
• Bogoliubov theory in the Gross-Pitaevskii limit
• Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
• Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger
• The energy of dilute Bose gases
• A microscopic derivation of time-dependent correlation functions of the \(1D\) cubic nonlinear Schrödinger equation
• Bose-Einstein condensation in a dilute, trapped gas at positive temperature
• Derivation of Hartree's theory for generic mean-field Bose systems
• Vortices in Bose-Einstein condensates
• Symmetric states of infinite tensor products of \(C^ *\)-algebras
• Symmetric Measures on Cartesian Products
• Bose-Einstein Condensation and Liquid Helium
• The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959
• The mean-field approximation in quantum electrodynamics: The no-photon case
• Equilibrium states for mean field models
• Locally normal symmetric states and an analogue of de Finetti's theorem
• Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits
• Bogoliubov Spectrum of Interacting Bose Gases
• Establishing Quantum Physics in Göttingen
• Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases
• The<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>Matrix in Quantum Electrodynamics
• Ground state energy of the one-component charged Bose gas.
• Renormalization of the regularized relativistic electron-positron field