Semiclassical wave packet dynamics in Schrodinger equations with periodic potentials

Abstract

We consider semiclassically scaled Schrodinger 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 obtained by Peierl's substitution, and involve a slowly varying envelope whose dynamics is governed by a homogenized Schrodinger equation with time-dependent effective mass. The corresponding adiabatic decoupling of the slow and fast degrees of freedom is shown to be valid up to Ehrenfest time scales.

15 pages. More explanations. An error fixed in the main result, to include the Berry phase

References in corpus (3)

• Semiclassical asymptotics for weakly nonlinear Bloch waves
• Quadratic Quantum Hamiltonians revisited
• Semiclassical Simple Initial Value Representations

Cited by in corpus (5)

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• Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature
• Frozen Gaussian approximation for high frequency wave propagation in periodic media
• Nonlinear dynamics of semiclassical coherent states in periodic potentials
• Soliton Pumping in the Rice-Mele Model with On-Cell Kerr Nonlinearity