KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
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AbstractWe consider a semiclassically scaled Schrödinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in measure) to the classical trajectories before the appearance of the first caustic. In a second step we show that after caustic onset this convergence in general no longer holds. In addition, we provide numerical simulations of the Bohmian trajectories in the semiclassical regime that illustrate the above results. © 2014 Wiley Periodicals, Inc.
SponsorsAF was supported by National Science Foundation Grant DMS-0969962. CK gives thanks for financial support to the ANR via the program ANR-09-BLAN-0117-01 and the project FroM-PDE funded by the European Research Council through the Advanced Investigator Grant Scheme. CS acknowledges support by the National Science Foundation through Grant DMS-1161580.