Dynamical correlations of two-dimensional vortex-like defects

High-order dynamical correlations of defects (quantum vortices, disclinations, etc.) in thin films are examined by starting from the Langevin equation for the defect motion. It is demonstrated that the dynamical correlation functions F2n of the vorticity or disclinicity behave as F2n∼y2/r4n, where r is the characteristic scale and y is the renormalized fugacity. Therefore below the Berezinskii-Kosterlitz-Thouless transition temperature the F2n are characterized by anomalous scaling exponents. The behavior differs strongly from the normal law F2n∼F2n obeyed by equal-time correlation functions; the unequal-time correlation functions appear to be much larger. The phenomenon resembles intermittency in turbulence.