Semiclassical approximations for adiabatic slow-fast systems

TL;DR

This paper systematically derives a semiclassical model for adiabatic slow-fast systems, incorporating Berry curvature effects, and demonstrates its accuracy in approximating quantum expectations and operator evolution, with applications to solid state physics.

Contribution

It provides a rigorous derivation and justification of the semiclassical model including Berry curvature corrections for adiabatic systems, extending previous work by Littlejohn and Flynn.

Findings

Classical Hamiltonian includes Berry curvature correction.

Model accurately approximates quantum expectations.

Application to Piezo-current in deformed crystals.

Abstract

In this letter we give a systematic derivation and justification of the semiclassical model for the slow degrees of freedom in adiabatic slow-fast systems first found by Littlejohn and Flynn [5]. The classical Hamiltonian obtains a correction due to the variation of the adiabatic subspaces and the symplectic form is modified by the curvature of the Berry connection. We show that this classical system can be used to approximate quantum mechanical expectations and the time-evolution of operators also in sub-leading order in the combined adiabatic and semiclassical limit. In solid state physics the corresponding semiclassical description of Bloch electrons has led to substantial progress during the recent years, see [1]. Here, as an illustration, we show how to compute the Piezo-current arising from a slow deformation of a crystal in the presence of a constant magnetic field.