Winding angle distribution of 2D random walks with traps

We study analytically the asymptotic behaviour of the average probability P(n,t) for the trajectory of a 2D Brownian particle wandering in the presence of randomly distributed traps to wind n times around a given point after a time t. It is shown that P(n,t)\sim\exp(-c\sqrt{t}) (1+x^2)^{-1} with x\sim n/\sqrt{t}, where the first exponent represents a well known long-time tail of the probability that a particle will not be trapped.Comment: RevTeX, 6 pages, 1 postscript figure, to be published in J. Phys.

Persistent current in a mesoscopic ring with diffuse surface scattering

The persistent current in a clean mesoscopic ring with ballistic electron motion is calculated. The particle dynamics inside a ring is assumed to be chaotic due to scattering at the surface irregularities of atomic size. This allows one to use the so-called ``ballistic'' supersymmetric \sigma model for calculation of the two-level correlation function in the presence of a nonzero magnetic flux.Comment: REVTeX, 4 pages; to be published in PRB (June 1999

Impurity resonances in the mixed state of high-Tc superconductors

We study the quasiparticle resonance states near strong impurities in the mixed state of a d-wave superconductor. These states give rise to zero-bias peaks in the local density of states, observed in scanning tunneling microscopy experiments. The field dependence of the peaks is obtained by averaging with respect to the spatially non-uniform Doppler shifts in the energy of excitations. The hybridization of the magnetic field-induced nodal quasiparticles with the impurity resonances results in the suppression and broadening of the zero-bias peaks. The height of the peaks is found to scale as \sqrt{Hc2/H}. The magnetic field response of the peaks is shown to be strongly dependent on the field orientation