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arXiv · 1010.4889

Semiclassical Propagation of Coherent States for the Hartree equation

Agissilaos Athanassoulis·Thierry Paul·Federica Pezzotti·Mario Pulvirenti
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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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Agissilaos Athanassoulis, Thierry Paul, Federica Pezzotti, Mario Pulvirenti. 2011-01-23. Semiclassical Propagation of Coherent States for the Hartree equation. https://doi.org/10.1007/s00023-011-0115-2

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