Tunnel Effect for Kramers-Fokker-Planck Type Operators: Return to Equilibrium and Applications

DOI10.1093/imrn/rnn057zbMath1151.35012arXiv0801.3615OpenAlexW1972729407MaRDI QIDQ3515940

Michael Hitrik, Frederic Hérau, Johannes Sjöstrand

Publication date: 30 July 2008

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3615

zbMATH Keywords

Fokker-Planck equationsemiclassical limitheat semigrouphypoellipticityreturn to equilibriumMorse functionWitten LaplacianKramers equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Hypoelliptic equations (35H10) Irreversible thermodynamics, including Onsager-Machlup theory (82B35)

Related Items (9)

Small eigenvalues of the low temperature linear relaxation Boltzmann equation with a confining potential ⋮ Null-controllability of hypoelliptic quadratic differential equations ⋮ Supersymmetric structures for second order differential operators ⋮ Return to Equilibrium, Non-self-adjointness and Symmetries, Recent Results with M. Hitrik and F. Hérau ⋮ Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning ⋮ Exponential return to equilibrium for hypoelliptic quadratic systems ⋮ Exact splitting methods for kinetic and Schrödinger equations ⋮ Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential ⋮ Around supersymmetry for semiclassical second order differential operators

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