On The Dynamics of Bohmian Measures
journal contributionposted on 2013-11-08, 00:00 authored by Peter Markowich, Christof Sparber, Thierry Paul
The present work is devoted to the study of dynamical features of Bohmian measures, recently introduced by the authors. We rigorously prove that for su ciently smooth wave functions the corresponding Bohmian measure furnishes a distributional solution of a nonlinear Vlasov-type equation. Moreover, we study the associated defect measures appearing in the classical limit. In one space dimension, this yields a new connection between monokinetic Wigner and Bohmian measures. In addition, we shall study the dynamics of Bohmian measures associated to so-called semi-classical wave packets. For these type of wave functions, we prove local in-measure convergence of a rescaled sequence of Bohmian trajectories towards the classical Hamiltonian flow on phase space. Finally, we construct an example of wave functions whose limiting Bohmian measure is not mono-kinetic but nevertheless equals the associated Wigner measure.
Publisher StatementPost print version of article may differ from published version. The final publication is available at springerlink.com; DOI: 10.1007/s00205-012-0528-1