Band functions of Iwatsuka models : power-like and flat magnetic fields
Spectral Theory
2018-10-01 v1
Abstract
In this note we consider the Iwatsuka model with a postive increasing magnetic field having finite limits. The associated magnetic Laplacian is fibred through partial Fourier transform, and, for large frequencies, the band functions tend to the Landau levels, which are thresholds in the spectrum. The asymptotics of the band functions is already known when the magnetic field converge polynomially to its limits. We complete this analysis by giving the asymptotics for a regular magnetic field which is constant at infinity, showing that the band functions converge now exponentially fast toward the thresholds. As an application, we give a control on the current of quantum states localized in energy near a threshold.
Keywords
Cite
@article{arxiv.1809.10958,
title = {Band functions of Iwatsuka models : power-like and flat magnetic fields},
author = {Nicolas Popoff and Pablo Miranda},
journal= {arXiv preprint arXiv:1809.10958},
year = {2018}
}