On an extension of the Iwatsuka model

TL;DR

This paper extends Iwatsuka's two-dimensional magnetic Hamiltonian model by including a translation-invariant electric field, proving absolute continuity and analyzing a quantum layer in a magnetic field.

Contribution

It introduces an extended class of magnetic Hamiltonians with electric fields and proves their absolute continuity, expanding the understanding of magnetic quantum systems.

Findings

Proved absolute continuity for the extended Hamiltonians.

Analyzed the effective Hamiltonian for a thin quantum layer.

Demonstrated the impact of electric fields on magnetic Hamiltonian properties.

Abstract

We prove absolute continuity for an extended class of two-dimensional magnetic Hamiltonians that were initially studied by A. Iwatsuka. In particular, we add an electric field that is translation invariant in the same direction as the magnetic field is. As an example, we study the effective Hamiltonian for a thin quantum layer in a homogeneous magnetic field.