Gauge optimization and spectral properties of magnetic Schr\"odinger operators
Spectral Theory
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We establish new necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schr\"odinger operators with a positive scalar potential. They extend earlier results by Maz'ya and Shubin (2005), which were obtained in case when there is no magnetic field. We also derive two-sided estimates for the bottoms of spectrum and essential spectrum, extending results by Maz'ya and Otelbaev (1977). The main idea is to optimize the gauge of the magnetic field, thus reducing the quadratic form to one without magnetic field (but with an appropriately adjusted scalar potential).
Keywords
Cite
@article{arxiv.math/0601057,
title = {Gauge optimization and spectral properties of magnetic Schr\"odinger operators},
author = {Vladimir Kondratiev and Vladimir Maz'ya and Mikhail Shubin},
journal= {arXiv preprint arXiv:math/0601057},
year = {2007}
}
Comments
20 pages