Geometrical phase for a three-dimensional anisotropic quantum well

TL;DR

This paper derives an explicit formula for the Berry phase in a 3D anisotropic quantum well subjected to a precessing magnetic field, using algebraic symplectic transformations.

Contribution

It introduces an algebraic algorithm to reduce quadratic Hamiltonians to canonical form for calculating Berry phases in complex quantum systems.

Findings

Explicit Berry phase formula for anisotropic quantum wells

Algebraic method for Hamiltonian reduction

Application to precessing magnetic fields

Abstract

A three-dimensional anisotropic quantum well placed in an adiabatically precessing uniform magnetic field is considered and an explicit formula for the Berry phase is obtained. To get the Berry phase, a purely algebraic algorithm of reducing a quadratic Hamiltonian to the canonical form via symplectic transformations of the phase space is presented.