Averaging of nonlinear Schr\"odinger equations with strong magnetic confinement

TL;DR

This paper derives an effective averaged model for nonlinear Schr"odinger equations under strong magnetic confinement, revealing spectral properties and deriving the LLL equation in a special case.

Contribution

It introduces an averaging technique to simplify the dynamics of nonlinear Schr"odinger equations with strong magnetic fields, connecting spectral analysis to effective models.

Findings

Derived an averaged nonlinear Schr"odinger model under magnetic confinement

Connected the model to the Landau Hamiltonian spectral properties

Provided a derivation of the LLL equation in a special case

Abstract

We consider the dynamics of nonlinear Schr\"odinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the Landau Hamiltonian. Using an averaging technique we derive an associated effective description via an averaged model of nonlinear Schr\"odinger type. In a special case this also yields a derivation of the LLL equation.