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Journal Articles Annales Henri Poincaré Year : 2011

Semiclassical Propagation of Coherent States for the Hartree equation

Abstract

In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in $L^2$ by $C \sqrt {\var}$, $\var$ being the Planck constant. Finally we present a full formal asymptotic expansion.
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Dates and versions

inria-00528993 , version 1 (23-10-2010)
inria-00528993 , version 2 (09-11-2010)
inria-00528993 , version 3 (23-01-2011)

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Agissilaos Athanassoulis, Thierry Paul, Federica Pezzotti, Mario Pulvirenti. Semiclassical Propagation of Coherent States for the Hartree equation. Annales Henri Poincaré, 2011, 12 (8), pp.1613-1634. ⟨10.1007/s00023-011-0115-2⟩. ⟨inria-00528993v3⟩
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