A quantum Boltzmann equation for Haldane statistics and hard forces; the space-homogeneous initial value problem

DOI10.1007/s00220-010-1046-3zbMath1203.82008OpenAlexW2090382993MaRDI QIDQ1958537

Yanyan Li

Publication date: 4 October 2010

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

Full work available at URL: https://doi.org/10.1007/s00220-010-1046-3

zbMATH Keywords

quantum Boltzmann-Haldane equation

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Quantum equilibrium statistical mechanics (general) (82B10) Boltzmann equations (35Q20)

Related Items (7)

Well-Posedness of the Cauchy Problem for a Space-Dependent Anyon Boltzmann Equation ⋮ Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮ On low temperature kinetic theory; spin diffusion, Bose Einstein condensates, anyons ⋮ On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮ Classical and quantum mechanical models of many-particle systems. Abstracts from the workshop held December 3--9, 2017 ⋮ On semi-classical limit of spatially homogeneous quantum Boltzmann equation: weak convergence ⋮ On a Boltzmann equation for Haldane statistics

Cites Work

• \(L^{\infty}\) estimates for the space-homogeneous Boltzmann equation
• On the spatially homogeneous Boltzmann equation
• Kinetic models and quantum effects: A modified Boltzmann equation for Fermi-Dirac particles
• Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II
• A modified Boltzmann equation for Bose-Einstein particles: Isotropic solutions and long-time behavior
• Haldane exclusion statistics and the Boltzmann equation
• Conservation of energy, entropy identity, and local stability for the spatially homogeneous Boltzmann equation
• ‘‘Fractional statistics’’ in arbitrary dimensions: A generalization of the Pauli principle

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