Random magnetic impurities and the Landau problem

Abstract

The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying α flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a transition, when α ≃ 0.3 − 0.4, from an "almost free" density of state -with only a depletion of states at the bottom of the spectrum characterized by a Lifschitz tail-to a Landau density of state with sharp Landau level oscillations. Several evidences and arguments for this transition -numerical and analyticalare presented.

Aharonov-Bohm effect on the Poincaré disk

“…This result has been first obtained in [10], and it has important consequences in the theory of disordered magnetic systems (see, for example, [13,14,15]). Obtaining the relation (5.11) directly from (5.10) is more subtle; one should consider ρ (ν)…”

“…In order to find the solution of the equation (2.13), consider the following ansatz: 14) where the signs "+" and "−" should be chosen for l ≥ 0 and l < 0, correspondingly. It is clear that the function, defined by (2.14), solves the equation (2.13) for t = t ′ and satisfies the boundary conditions of square integrability at the points t = 0 and t = 1.…”

Paraxial propagation of a quantum charge in a random magnetic field

“…The random field is assumed to be weak in the sense that L much exceeds the wave length λ ≡h/p, p being the particle momentum. In another model [20][21][22] which is motivated by fractional statistics theories, the gauge potential is created by a random array of the Aharonov-Bohm flux lines. A system of the Abrikosov vortices (e.g.…”

The spectrum of Schrödinger operators with random \delta magnetic fields

“…In the present paper, we consider the case there is some randomness in the positions of δ magnetic fields or in their intensities, and study some fundamental spectral properties of the Schrödinger operators with random δ magnetic fields. The system of this type is studied in some physics literature [17], [18], [10], [11], [12], but there seems no mathematical results at present. BorgPulé [8] studied a similar system (Pauli operators with smoothed random Aharonov-Bohm fields).…”

“…-The authors thank to Prof. L. Pastur for introducing us the paper [9], and also thank to J.L. Borg for introducing us the papers [8], [17], [18], [10], [11], [12].…”