Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)

TL;DR

This paper develops a quantum guiding center theory for charged spinning particles in inhomogeneous magnetic fields, enabling systematic analysis of their different time scale behaviors and effective dynamics.

Contribution

It introduces a new quantal guiding center framework with operators adapted to inhomogeneous fields, expanding on previous homogeneous field models.

Findings

Rewrites the Pauli Hamiltonian as a power series in magnetic length

Constructs the first two terms of the series explicitly

Identifies gauge fields and scalar potentials in effective dynamics

Abstract

A quantal guiding center theory allowing to systematically study the separation of the different time scale behaviours of a quantum charged spinning particle moving in an external inhomogeneous magnetic filed is presented. A suitable set of operators adapting to the canonical structure of the problem and generalizing the kinematical momenta and guiding center operators of a particle coupled to a homogenous magnetic filed is constructed. The Pauli Hamiltonian rewrites in this way as a power series in the magnetic length $l_B= \sqrt{\hbar c/eB}$ making the problem amenable to a perturbative analysis. The first two terms of the series are explicitly constructed. The effective adiabatic dynamics turns to be in coupling with a gauge filed and a scalar potential. The mechanism producing such magnetic-induced geometric-magnetism is investigated in some detail.