Bohmian measures and their classical limit |
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Authors: | Peter Markowich |
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Institution: | a Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, United Kingdom b CNRS and Centre de mathématiques Laurent Schwartz, École Polytechnique, 91 128 Palaiseau cedex, France |
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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. |
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Keywords: | Quantum mechanics Wigner function Bohmian mechanics Classical limit Young measures Weak convergence |
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