Semiclassical Analysis for the Kramers–Fokker–Planck Equation

DOI10.1081/PDE-200059278zbMath1083.35149arXivmath/0406275MaRDI QIDQ5314608

Christiaan C. Stolk, Johannes Sjöstrand, Frederic Hérau

Publication date: 5 September 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406275

zbMATH Keywords

Fokker-Planck equationWeyl calculuscritical pointsFBI-Bargmann transformpseudo-spectrumKramers equation

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Spectrum, resolvent (47A10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Pseudodifferential operators (47G30) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (26)

Semiclassical Gevrey operators and magnetic translations ⋮ Small eigenvalues of the low temperature linear relaxation Boltzmann equation with a confining potential ⋮ Geometric Fokker-Planck equations. II: Maximal hypoelliptic estimates ⋮ \(L^{2}\)-regularity of kinetic equations with external potential ⋮ Spectra and semigroup smoothing for non-elliptic quadratic operators ⋮ Spectral projections and resolvent bounds for partially elliptic quadratic differential operators ⋮ The semiclassical regime for ablation front models ⋮ Global hypoelliptic estimates for Landau-type operators with external potential ⋮ Short and long time behavior of the Fokker-Planck equation in a confining potential and applications ⋮ Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics ⋮ From semigroups to subelliptic estimates for quadratic operators ⋮ Return to Equilibrium, Non-self-adjointness and Symmetries, Recent Results with M. Hitrik and F. Hérau ⋮ Semiclassical Gevrey operators in the complex domain ⋮ Regularity of the spatially homogenous fractional Kramers-Fokker-Planck equation ⋮ Null-controllability properties of the generalized two-dimensional Baouendi-Grushin equation with non-rectangular control sets ⋮ Exponential return to equilibrium for hypoelliptic quadratic systems ⋮ Precise Arrhenius law for \(p\)-forms: the Witten Laplacian and Morse-Barannikov complex ⋮ Large time behaviour for the Fokker-Planck equation with general potential ⋮ Subelliptic resolvent estimates for non-self-adjoint semiclassical Schrödinger operators ⋮ Tunnel effect and symmetries for Kramers–Fokker–Planck type operators ⋮ Anisotropic hypoelliptic estimates for Landau-type operators ⋮ Semiclassical Hypoelliptic Estimates for Non-Selfadjoint Operators with Double Characteristics ⋮ Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential ⋮ Resolvent Estimates for Non-Selfadjoint Operators via Semigroups ⋮ Semigroup expansions for non-selfadjoint Schrödinger operators ⋮ Positivity, complex FIOs, and Toeplitz operators

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