Dynamics of Bloch Electrons in Time Dependent External Electric Fields: Bounds for Interband Transitions

TL;DR

This paper derives upper bounds for interband transitions of Bloch electrons under slowly varying electric fields, supporting the long-term validity of the one-band approximation in such conditions.

Contribution

It introduces adiabatic expansion formalism to establish bounds on interband transitions, enhancing understanding of electron dynamics in time-dependent fields.

Findings

Interband transition bounds are established for slowly varying electric fields.

The results validate the one-band approximation over extended time periods.

The formalism provides a rigorous framework for analyzing electron dynamics in external fields.

Abstract

Using adiabatic expansions formalism, upper bounds for interband transitions for Bloch electrons in slowly varying in time electric fields are obtained. These bounds imply the validity of one-band approximation on long time scales.