Berry phase from a randomly fluctuating magnetic field

Abstract

The quantum-mechanical Berry phase due to a randomly fluctuating magnetic field is calculated by exploiting an analogous random-walk problem in polymer physics. The phase depends on the time correlations of the magnetic field, despite the adiabatic nature of the Berry phase. A probability distribution for the phase is obtained, and how this phase could affect the magnetotransport in granular magnetic nanostructures is briefly discussed.