On the time evolution of Wigner measures for Schrödinger equations

DOI10.3934/cpaa.2009.8.559zbMath1159.81034arXiv0803.0667OpenAlexW3103398194MaRDI QIDQ1006194

Hans Peter Stimming, Rémi Carles, Norbert J. Mauser, Clotilde Fermanian-Kammerer

Publication date: 20 March 2009

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.0667

zbMATH Keywords

Schrödinger equationsemi-classical limitill-posednesscausticWigner measureseigenvalue crossingWKB methods

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

Related Items (9)

Semiclassical evolution of quantum wave packets on the torus beyond the Ehrenfest time in terms of Husimi distributions ⋮ Gabor products and a phase space approach to nonlinear analysis ⋮ One-scale H-distributions and variants ⋮ Wavepackets in inhomogeneous periodic media: Effective particle-field dynamics and Berry curvature ⋮ Classical limit for a system of non-linear random Schrödinger equations ⋮ Wigner measures supported on weak KAM tori ⋮ Convergence rate in Wasserstein distance and semiclassical limit for the defocusing logarithmic Schrödinger equation ⋮ Localisation principle for one-scale H-measures ⋮ Coarse-scale representations and smoothed Wigner transforms

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