On the dynamics of Bohmian measures - Archive ouverte HAL
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2012

On the dynamics of Bohmian measures

Résumé

We revisit the concept of Bohmian measures recently introduced by the authors in \cite{MPS}. 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.
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Dates et versions

hal-00539227 , version 1 (24-11-2010)

Identifiants

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Peter Markowich, Thierry Paul, Christof Sparber. On the dynamics of Bohmian measures. Archive for Rational Mechanics and Analysis, 2012, 205 (3), pp.1031-1054. ⟨10.1007/s00205-012-0528-1⟩. ⟨hal-00539227⟩
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