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Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data
Author(s) -
Ambrosio Luigi,
Figalli Alessio,
Friesecke Gero,
Giannoulis Johannes,
Paul Thierry
Publication year - 2011
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20371
Subject(s) - semiclassical physics , uniqueness , mathematics , measure (data warehouse) , limit (mathematics) , schrödinger equation , space (punctuation) , quantum , mathematical analysis , flow (mathematics) , initial value problem , dynamics (music) , stability (learning theory) , mathematical physics , quantum mechanics , physics , geometry , database , machine learning , computer science , acoustics , linguistics , philosophy
In 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. © 2011 Wiley Periodicals, Inc.