Berry phase correction to electron density in solids and "exotic" dynamics

TL;DR

This paper explains recent semiclassical electron dynamics in solids using exotic Galilean dynamics, showing the system's Hamiltonian nature and deriving hydrodynamic equations for certain quantities.

Contribution

It introduces a Hamiltonian framework for electron dynamics in solids incorporating Berry phase effects, connecting it with exotic Galilean mechanics.

Findings

Electron dynamics are Hamiltonian with preserved symplectic volume.

Hydrodynamic equations are derived for relevant physical quantities.

The approach unifies semiclassical and exotic Galilean dynamics.

Abstract

Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for ``exotic'' Galilean dynamics. The system is indeed Hamiltonian and Liouville's theorem holds for the symplectic volume form. Suitably defined quantities satisfy hydrodynamic equations.