A variational formula for the free energy of an interacting many-particle system

DOI10.1214/10-AOP565zbMath1225.60147arXiv1003.1393OpenAlexW2028012704MaRDI QIDQ2431522

Andrea Collevecchio, Wolfgang König, Stefan Adams

Publication date: 15 April 2011

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.1393

zbMATH Keywords

free energyBrownian bridgevariational formulasymmetrized distributioninteracting many-particle systems, Bose-Einstein condensationlarge deviations, empirical stationary measure

Mathematics Subject Classification ID

Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10) Path integrals in quantum mechanics (81S40) Quantum equilibrium statistical mechanics (general) (82B10)

Related Items (14)

Phase transitions in Delaunay Potts models ⋮ Large deviations analysis for random combinatorial partitions with counter terms ⋮ Large deviations in weakly interacting fermions: Generating functions as Gaussian Berezin integrals and bounds on large Pfaffians ⋮ Macroscopic loops in the Bose gas, spin \(O(N)\) and related models ⋮ Upper large deviations for power-weighted edge lengths in spatial random networks ⋮ Formation of infinite loops for an interacting bosonic loop soup ⋮ Emergence of interlacements from the finite volume Bose soup ⋮ A micro-macro variational formula for the free energy of a many-body system with unbounded marks ⋮ Interplay of analysis and probability in applied mathematics. Abstracts from the workshop held February 11--17, 2018 ⋮ Randomization and the Gross-Pitaevskii hierarchy ⋮ Space-time random walk loop measures ⋮ Local existence of solutions to randomized Gross-Pitaevskii hierarchies ⋮ An explicit large deviation analysis of the spatial cycle Huang-Yang-Luttinger model ⋮ Functional integral and stochastic representations for ensembles of identical bosons on a lattice

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The mathematics of the Bose gas and its condensation.
• Statistical mechanics of combinatorial partitions, and their limit shapes
• Asymptotic Feynman-Kac formulae for large symmetrised systems of random walks
• Large deviations for many Brownian bridges with symmetrised initial-terminal condition
• Gibbs measures and phase transitions
• Large deviations and the maximum entropy principle for marked point random fields
• Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction
• Long cycles in a perturbed mean field model of a Boson gas
• Spatial random permutations and infinite cycles
• Limit theorems for statistics of combinatorial partitions with applications to mean field Bose gas
• On the Position Distribution of the Ideal Bose Gas
• Percolation transition in the Bose gas: II
• Atomic Theory of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi></mml:math>Transition in Helium

This page was built for publication: A variational formula for the free energy of an interacting many-particle system