Semiclassical Propagation of Coherent States for the Hartree equation

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.

References in corpus (3)

• Mean-Field Dynamics: Singular Potentials and Rate of Convergence
• Nonlinear coherent states and Ehrenfest time for Schrodinger equation
• The evolution operator of the Hartree-type equation with a quadratic potential

Cited by in corpus (5)

• The Schrödinger Equation in the Mean-Field and Semiclassical Regime
• Empirical Measures and Quantum Mechanics: Application to the Mean-Field Limit
• Semiclassical approach to the nonlocal nonlinear Schrödinger equation with a non-Hermitian term
• Quasiparticle solutions for the nonlocal NLSE with an anti-Hermitian term in semiclassical approximation
• Interaction of coherent states for Hartree equations