Semiclassical Propagation of Coherent States for the Hartree equation

Agissilaos Athanassoulis; Thierry Paul; Federica Pezzotti; Mario Pulvirenti

inria-00528993, version 3

Semiclassical Propagation of Coherent States for the Hartree equation

Agissilaos Athanassoulis () ¹, Thierry Paul ¹, Federica Pezzotti ², Mario Pulvirenti ³

(2010)

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.

1: Centre de Mathématiques Laurent Schwartz (CMLS-EcolePolytechnique)
CNRS : UMR7640 – Polytechnique - X
2: Departamento de Matematicas
Universidad del Pais Vasco- Euskal Herriko Unibertsitatea
3: Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
Universita di Roma "La Sapienza"

inria-00528993, version 3
http://hal.inria.fr/inria-00528993
oai:hal.inria.fr:inria-00528993
From: Agissilaos Athanassoulis <>
Submitted on: Sunday, 23 January 2011 15:27:49
Updated on: Sunday, 23 January 2011 16:52:35

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