Bohmian measures and their classical limit

Type
Article

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

KAUST Grant Number
KUK-I1-007-43

Date
2010-09

Abstract
We consider a class of phase space measures, which naturally arise in the Bohmian interpretation of quantum mechanics. We study the classical limit of these so-called 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. Our analysis gives new insight on oscillation and concentration effects in the semi-classical regime. © 2010 Elsevier Inc.

Citation
Markowich P, Paul T, Sparber C (2010) Bohmian measures and their classical limit. Journal of Functional Analysis 259: 1542–1576. Available: http://dx.doi.org/10.1016/j.jfa.2010.05.013.

Acknowledgements
This publication is based on work supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST). Christof Sparber has been supported by the Royal Society via his University research fellowship and Peter Markowich by his Royal Society Wolfson Research Merit Award.

Publisher
Elsevier BV

Journal
Journal of Functional Analysis

DOI
10.1016/j.jfa.2010.05.013

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