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Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data

Abstract : n this paper we study the semiclassical limit of the Schrodinger equation. Under mild regularity assumptions on the potential U, which include Born-Oppenheimer potential energy surfaces in molecular dynamics, we establish asymptotic validity of classical dynamics globally in space and time for "almost all" initial data, with respect to an appropriate reference measure on the space of initial data. In order to achieve this goal we prove existence, uniqueness, and stability results for the flow in the space of measures induced by the continuity equation
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https://hal.archives-ouvertes.fr/hal-00851540
Contributor : Carole Juppin <>
Submitted on : Wednesday, August 14, 2013 - 5:42:26 PM
Last modification on : Monday, October 12, 2020 - 10:27:29 AM

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  • HAL Id : hal-00851540, version 1

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Luigi Ambrosio, Alessio Figalli, Gero Friesecke, Johannes Giannoulis, Thierry Paul. Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data. Communications on Pure and Applied Mathematics, Wiley, 2011, 64 (9), pp.1199-1242. ⟨hal-00851540⟩

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