Georgi Raikov

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We consider the Schrödinger operator H(V ) on L(R) or L(R), with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V ) near the boundary points of its essential spectrum. If the decay of V is Gaussian or(More)
We consider the three-dimensional Schrödinger operator H with constant magnetic field of strength b > 0 and continuous electric potential V ∈ L(R) which admits certain power-like estimates at infinity. We study the asymptotic behaviour as b→∞, of the spectral shift function ξ(E;H,H0) for the pair of operators (H,H0) at energies E = Eb+ λ, E > 0 and λ ∈ R(More)
We consider the three-dimensional Schrödinger operator with constant magnetic field and bounded random electric potential. We investigate the asymptotic behaviour of the integrated density of states for this operator as the norm of the magnetic field tends to infinity. Résumé On considère l’opérateur de Schrödinger tridimensionnel avec un champ magnétique(More)
We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized Iwatsuka potentials. In both cases we prove quantization of the edge conductance. Next, we consider magnetic perturbations of such magnetic barriers or guides, and(More)
We consider a 2D Schrödinger operator H0 with constant magnetic field, on a strip of finite width. The spectrum of H0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H0 by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H = H0 + V . First, we(More)
Abstract: We consider the 2D Landau Hamiltonian H perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of H. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like,(More)
We consider the three-dimensional Schrödinger operator with constant magnetic field, perturbed by an appropriate short-range electric potential, and investigate various asymptotic properties of the corresponding spectral shift function (SSF). First, we analyse the singularities of the SSF at the Landau levels. Further, we study the strong magnetic field(More)
We consider the unperturbed operator H0 := (−i∇ − A)2 + W , self-adjoint in L2(R2). Here A is a magnetic potential which generates a constant magnetic field b > 0, and the edge potential W is a non-decreasing non constant bounded function depending only on the first coordinate x ∈ R of (x, y) ∈ R2. Then the spectrum of H0 has a band structure and is(More)