Semiclassical wave packet dynamics in
Schrödinger equations with periodic potentials
Rémi Carles - CNRS & Univ. Montpellier 2, Mathématiques, CC 051, 34095 Montpellier, France (email)
Abstract: We consider semiclassically scaled Schrödinger equations with an external potential and a highly oscillatory periodic potential. We construct asymptotic solutions in the form of semiclassical wave packets. These solutions are concentrated (both, in space and in frequency) around the effective semiclassical phase-space flow, and involve a slowly varying envelope whose dynamics is governed by a homogenized Schrödinger equation with time-dependent effective mass tensor. The corresponding adiabatic decoupling of the slow and fast degrees of freedom is shown to be valid up to Ehrenfest time scales.
Keywords: Schrödinger equation, semiclassical wave packet, periodic
potential, Bloch band, Ehrenfest time.
Received: March 2011; Revised: November 2011; Published: January 2012.
2011 Impact Factor.921