Semiclassical Propagation of Coherent States for the Hartree equation

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

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Departamento de Matematicas
3 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

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.

Mots clés: Hartree equation; Coherent states; Semiclassical analysis

Domaines: Equations aux dérivées partielles [math.AP]

Agissilaos Athanassoulis, Thierry Paul, Federica Pezzotti, Mario Pulvirenti. Semiclassical Propagation of Coherent States for the Hartree equation. 2010. ⟨inria-00528993v2⟩