
Abstract
We consider a two-dimensional massless Dirac operator H in the presence of a perturbed homogeneous magnetic field B = B-0 + b and a scalar electric potential V. For V is an element of L-loc(p) (R-2), p is an element of(2, infinity], and b is an element of L-loc(q)(R-2), q is an element of(1, infinity], both decaying at infinity, we show that states in the discrete spectrum of H are superexponentially localized. We establish the existence of such states between the zeroth and the first Landau level assuming that V = 0. In addition, under the condition that b is rotationally symmetric and that V satisfies certain analyticity condition on the angular variable, we show that states belonging to the discrete spectrum of H are Gaussian-like localized.
Item Type: | Journal article |
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Form of publication: | Publisher's Version |
Keywords: | Magnetic operator; localization; Dirac operator |
Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
Subjects: | 500 Science > 510 Mathematics |
URN: | urn:nbn:de:bvb:19-epub-23156-1 |
ISSN: | 1664-039X |
Alliance/National Licence: | This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively. |
Language: | English |
Item ID: | 23156 |
Date Deposited: | 02. Mar 2015, 10:38 |
Last Modified: | 13. Aug 2024, 12:41 |