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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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https://hal.inria.fr/inria-00528993
Contributor : Agissilaos Athanassoulis Connect in order to contact the contributor
Submitted on : Sunday, January 23, 2011 - 3:27:49 PM
Last modification on : Wednesday, November 3, 2021 - 2:18:08 PM
Long-term archiving on: : Sunday, April 24, 2011 - 2:45:03 AM

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

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