Dynamics of one-dimensional tight-binding models with arbitrary time-dependent external homogeneous fields

TL;DR

This paper derives exact propagators for 1D tight-binding models under arbitrary time-dependent homogeneous fields, generalizes the Bloch acceleration theorem, and shows wave packet shape preservation and control via pulsed fields.

Contribution

It provides exact solutions for time-dependent fields, extending the Bloch theorem and demonstrating wave packet control in quantum lattice systems.

Findings

Exact propagators for time-dependent fields derived

Wave packets maintain shape under arbitrary fields

Pulsed fields can stop or accelerate wave packets

Abstract

The exact propagators of two one-dimensional systems with time-dependent external fields are presented by following the path-integral method. It is shown that the Bloch acceleration theorem can be generalized to the impulse-momentum theorem in quantum version. We demonstrate that an evolved Gaussian wave packet always keeps its shape in an arbitrary time-dependent homogeneous driven field. Moreover, that stopping and accelerating of a wave packet can be achieved by the pulsed field in a diabatic way.