Particle in a random magnetic field on a plane

Abstract

We study the properties of a two-dimensional spinless particle moving in a random magnetic field. This problem arises in the context of a modern theory of strongly correlated systems as well as in the theory of vortex-lines dynamics in high-T, materials. The problem is investigated with a variety of methods including direct perturbation theory, quasiclassical approximation, the method of an optimal fluctuation, and Monte Carlo simulations. We obtain a shape of the density of states near the unrenormalized lower boundary of the spectrum, a particle mobility, and its diamagnetic orbital susceptibility.

Paraxial propagation of a quantum charge in a random magnetic field

“…In recent years, the random magnetic field problem has been an active subject area Refs. [11][12][13][14][15][16][17][18][19].…”

Single-Particle Relaxation in a Random Magnetic Field

“…It was shown there that although the single particle relaxation rate 1/τ is plagued by infrared divergence problems, the electrical conductivity is determined by the transport (momentum) relaxation time τ tr , which can be calculated perturbatively (see also [8]) . As far as the critical behavior of the model is concerned, the problem could be mapped onto a nonlinear supersymmetric σ-model of interacting matrices with unitary symmetry.…”

Tails of the density of states in a random magnetic field

“…Moreover, in the case of RMF, the perturbative approach is also fundamentally problematic since one has to deal with the non-diagonal part of the Green function, which is not gauge invariant. In addition, the calculation of the Green function is plagued by infrared divergencies [7,8,9,10,11] that are due to the long-range nature of the correlations of the vector potential, even if the spatial correlations in the RMF are short-ranged. It has been suggested that these divergencies are due to the non-gauge-invariance of the Green function and therefore unphysical [9], although, recently, a physical interpretation has been proposed [11].…”

“…Also, it should exceed Γ, the disorder induced width of the Landau Levels (LL). A field theoretical approach has been used to determine the DOS in a RMF with zero mean value near the band edge [8]. The tail of the DOS in a system of randomly distributed flux tubes of fixed strength was considered [13].…”