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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
• oai:hal.inria.fr:inria-00528993
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• Submitted on: Sunday, 23 January 2011 15:27:49
• Updated on: Sunday, 23 January 2011 16:52:35