The Kosterlitz-Thouless transition and vortex dynamics

Abstract

The physics of the Kosterlitz-Thouless vortex-unbinding transition in two-dimensional superfluids is discussed, and the N × N Josephson junction array is considered as a prototype system. Dynamical behaviour is considered in two cases: (a) the complex impedance shows structure at a frequency-dependent transition temperature, similar to the dynamic susceptibility of a spin glass; (b) with a perpendicular non-uniform magnetic field, of a particular 'self-similar' hierarchical pattern, a scaling argument gives non-exponential relaxational dynamics of a prepared non-equilibrium vortex distribution.