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The integrated density of states in strong magnetic fields
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2006-08-15)
We consider three-dimensional Schrodinger operators with constant magnetic fields and ergodic electric potentials. We study the strong magnetic field asymptotic behaviour of the integrated density of states, distinguishing ...
Discrete spectrum of quantum Hall effect Hamiltonians II: Periodic edge potentials
(IOS PRESS, 2012)
We consider the unperturbed operator H-0 := (-i del-A)(2) + W, self-adjoint in L-2(R-2). Here A is a magnetic potential which generates a constant magnetic field b > 0, and the edge potential W = (W) over bar is a T-periodic ...
On eigenvalue accumulation for non-self-adjoint magnetic operators
(ELSEVIER SCIENCE BV, 2017)
In this work, we use regularized determinants to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schrodinger operator (-i del - A)(2) -b in R-3, with constant ...
Resonances and spectral shift function near the Landau levels
(ANNALES DE L INSTITUT FOURIER, 2007)
We consider the 3D Schrodinger operator H = H-0 + V where H-0 = (-i del - A)(2) - b, A is a magnetic potential generating a constant magneticfield of strength b > 0, and V is a short-range electric potential which decays ...
Spectral properties of a magnetic quantum Hamiltonian on a strip
(IOS PRESS, 2008)
We consider a 2D Schrodinger operator H(0) with constant magnetic field, on a strip of finite width. The spectrum of H(0) is absolutely continuous, and contains a discrete set of thresholds. We perturb H(0) by an electric ...
Asymptotics Near +/- m of the Spectral Shift Function for Dirac Operators with Non-Constant Magnetic Fields
(TAYLOR & FRANCIS INC, 2011)
We consider a 3-dimensional Dirac operator H0 with non-constant magnetic field of constant direction, perturbed by a sign-definite matrix-valued potential V decaying fast enough at infinity. Then we determine asymptotics, ...
The Fate of the Landau Levels under Perturbations of Constant Sign
(OXFORD UNIV PRESS, 2009)
We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrodinger operator with a constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not ...
Spectral shift function for magnetic schrodinger operators
(SPRINGER, 2006)