Averaging of nonlinear Schr\"odinger equations with strong magnetic confinement
Mathematical Physics
2018-12-18 v2 Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.1611.01574,
title = {Averaging of nonlinear Schr\"odinger equations with strong magnetic confinement},
author = {Rupert L. Frank and Florian Méhats and Christof Sparber},
journal= {arXiv preprint arXiv:1611.01574},
year = {2018}
}
Comments
12 pages; some references added; some typos corrected