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We have calculated wave functions and matrix elements of the dipole operator in the two- and three-dimensional Anderson model of localization and have studied their statistical properties in the limit of weak disorder. In particular, we…

Disordered Systems and Neural Networks · Physics 2025-10-01 Ville Uski , Bernhard Mehlig , Rudolf A. Roemer

In this paper, we first improve some asymptotic formulas previously obtained and provide sharp asymptotic formulas explicitly expressed by the potential. For the potentials of bounded variation, we obtain asymptotic formulas in which the…

Spectral Theory · Mathematics 2025-12-17 Cemile Nur , Oktay Veliev

We consider the Stokes eigenvalue problem in a bounded domain of R3 with Dirich- let boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the boundary perturbations of…

Mathematical Physics · Physics 2016-12-22 Christian Daveau , Abdessatar Khelifi

We propose a simple situation in which the magnetic Aharonov-Bohm potential influences the values of the deficiency indices of the initial Schr\"odinger operator, so determining whether the particle interacts with the solenoid or not. Even…

Mathematical Physics · Physics 2020-02-12 Cesar R. de Oliveira , Renan G. Romano

The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux…

Quantum Physics · Physics 2009-10-31 H. -P. Thienel

We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…

Mathematical Physics · Physics 2015-07-24 Christian Engström , Heinz Langer , Christiane Tretter

We study an inverse boundary value problem with partial data in an infinite slab in $\mathbb{R}^{n}$, $n\geq 3$, for the magnetic Schr\"{o}dinger operator with an $L^{\infty}$ magnetic potential and an $L^{\infty}$ electric potential. We…

Analysis of PDEs · Mathematics 2013-11-12 Shitao Liu , Yang Yang

In the present article we analyze the bound states of an electron in a Coulomb field when an Aharonov-Bohm field as well as a magnetic Dirac monopole are present. We solve, via separation of variables, the Schr\"odinger equation in…

High Energy Physics - Theory · Physics 2009-10-28 Victor M. Villalba

In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…

Spectral Theory · Mathematics 2025-12-16 Vincent Bruneau , Pablo Miranda

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading…

Analysis of PDEs · Mathematics 2009-11-11 Youcef Amirat , Gregory A. Chechkin , Rustem R. Gadyl'shin

Observations of clusters of galaxies show ubiquitous presence of X-ray cavities, presumably blown by the AGN jets. We consider magnetic field structures of these cavities. Stability requires that they contain both toroidal and poloidal…

High Energy Astrophysical Phenomena · Physics 2015-05-19 Konstantinos Nektarios Gourgouliatos , Jonathan Braithwaite , Maxim Lyutikov

A manifestation of the many-body Aharonov-Bohm effect in the magnetic-flux-tuned Mott insulators with three-spin and four-spin ring exchanges, presents as an effective tool to manipulate the ground-state spin chirality, such as, tune the…

Strongly Correlated Electrons · Physics 2010-11-02 Yi-Fei Wang , Chang-De Gong

We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper…

Spectral Theory · Mathematics 2018-04-17 Evgeny Korotyaev , Oleg Safronov

On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions.…

Analysis of PDEs · Mathematics 2014-06-19 Jonathan Rohleder

The experimental realization of a coupled spin pair has been reported by Heiko Webber et.al and its theoretical description has been previously discussed including the condition that local magnetization of the junction is required for the…

Mesoscale and Nanoscale Physics · Physics 2019-10-23 Juan David Vasquez Jaramillo , Erik Sjoqvist , Jonas Fransson

In this note the three dimensional Dirac operator $A_m$ with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that $A_m$ is self-adjoint in…

Spectral Theory · Mathematics 2021-02-01 Markus Holzmann

By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained,…

Complex Variables · Mathematics 2013-07-25 Timothy H. McNicholl

The Aharonov-Bohm effect is investigated in two-dimensional, single-terminal quantum rings in magnetic fields by using time-dependent density-functional theory. We find multiple transport loops leading to the oscillation periods of h/(en),…

Strongly Correlated Electrons · Physics 2010-06-22 V. Kotimaki , E. Rasanen

We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\mathbb{R}^{2d}$, $d\geq 1$. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give…

Mathematical Physics · Physics 2015-05-13 Mikael Persson

Magneto-transport properties are investigated in a binary alloy ring subjected to an Aharonov-Bohm (AB) flux \phi within a single-band non-interacting tight-binding framework. In the first part, we expose analytically the behavior of…

Mesoscale and Nanoscale Physics · Physics 2012-04-10 Paramita Dutta , Santanu K. Maiti , S. N. Karmakar