On the Dynamics of Bohmian Measures

Peter A. Markowich, Thierry A. Paul, Christof Sparber

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The present work is devoted to the study of dynamical features of Bohmian measures, recently introduced by the authors. We rigorously prove that for sufficiently 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 mono-kinetic 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. © 2012 Springer-Verlag.
Original languageEnglish (US)
Pages (from-to)1031-1054
Number of pages24
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - May 8 2012

ASJC Scopus subject areas

  • Mechanical Engineering
  • Analysis
  • Mathematics (miscellaneous)


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