BOHMIAN MEASURES AND THEIR CLASSICAL LIMIT

Peter Markowich (1) , Thierry Paul (2) , Christof Sparber (1)

1 DAMTP - Department of Applied Mathematics and Theoretical Physics
2 CMLS - Centre de Mathématiques Laurent Schwartz

We consider a class of phase space measures, which naturally arise in the Bohmian interpretation of quantum mechanics (when written in a Lagrangian form). We study the so-called classical limit of these Bohmian measures, in dependence on the scale of oscillations and concentrations of the sequence of wave functions under consideration. The obtained results are consequently compared to those derived via semi-classical Wigner measures. To this end, we shall also give a connection to the theory of Young measures and prove several new results on Wigner measures themselves. We believe that our analysis sheds new light on the classical limit of Bohmian quantum mechanics and gives further insight on oscillation and concentration eects of semi-classical wave functions.

Domaines: Equations aux dérivées partielles [math.AP]

Peter Markowich, Thierry Paul, Christof Sparber. BOHMIAN MEASURES AND THEIR CLASSICAL LIMIT. 2010. ⟨hal-00496378⟩