Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics

TL;DR

This paper derives the Hamiltonian for the quantum Hall effect on manifolds with nonconstant metrics, calculates its spectrum and eigenfunctions, and explores applications on hyperbolic spaces.

Contribution

It provides a closed-form Hamiltonian and spectral analysis for quantum Hall systems on hyperbolic and other nonconstant metric spaces, extending previous flat-space models.

Findings

Hamiltonian derived for hyperbolic metric spaces

Spectrum and eigenfunctions calculated explicitly

Applications discussed for hyperbolic disks

Abstract

The problem of studying the quantum Hall effect on manifolds with nonconstant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well.