Winding of a two-dimensional Brownian particle in a random environment
Abstract
We study analytically the average probability for a Brownian particle to wind n times around a removed area of finite size in a 2D plane with randomly distributed traps. Such a model describes, for example, the Abrikosov vortex entanglement around a cylindrical cavity in a superconductor with repulsive columnar defects. The problem amounts to the quantum mechanics of a particle moving in a plane with point-like random scatterers pierced by a solenoid. It is shown that at large times t the asymptotic winding angle distribution, which is determined by a `Lifshitz tail' in the density of states of such a particle, is Gaussian with the scaling variable 0305-4470/31/47/007/img1.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- November 1998
- DOI:
- 10.1088/0305-4470/31/47/007
- Bibcode:
- 1998JPhA...31.9455S