THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR

DOI10.1142/S0218202512500340zbMath1253.82065arXiv1010.2791MaRDI QIDQ4649854

Clément Mouhot, Stéphane Mischler, Maria Pia Gualdani, Anton Arnold, Christof Sparber, Irene Martínez Gamba

Publication date: 15 November 2012

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2791

zbMATH Keywords

spectral gapstationary solutionlarge-time behaviorWigner transformFokker-Planck operator

Mathematics Subject Classification ID

Long-time behavior of solutions for dynamical problems in solid mechanics (74H40) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Perturbation theories for operators and differential equations in quantum theory (81Q15) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (11)

Spectral analysis of semigroups and growth-fragmentation equations ⋮ Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach ⋮ Instability in a Vlasov-Fokker-Planck binary mixture ⋮ Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems ⋮ The Wigner(–Poisson)–Fokker–Planck equation with singular potential ⋮ Spectral analysis and long-time behaviour of a Fokker-Planck equation with a non-local perturbation ⋮ A stochastic algorithm without time discretization error for the Wigner equation ⋮ Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential ⋮ Stability analysis of quantum systems: a Lyapunov criterion and an invariance principle ⋮ A Mean-Field Model for Spin Dynamics in Multilayered Ferromagnetic Media ⋮ Convergence to pure steady states of linear quantum systems

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