Semiclassical Propagation of Coherent States for the Hartree equation
Mathematical Physics
2015-05-19 v3 math.MP
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 by , being the Planck constant. Finally we present a full formal asymptotic expansion.
Keywords
Cite
@article{arxiv.1010.4889,
title = {Semiclassical Propagation of Coherent States for the Hartree equation},
author = {Agissilaos Athanassoulis and Thierry Paul and Federica Pezzotti and Mario Pulvirenti},
journal= {arXiv preprint arXiv:1010.4889},
year = {2015}
}