Intermittency in Dynamics of Two-Dimensional Vortex-like Defects

Abstract

We examine high-order dynamical correlations of defects (vortices, disclinations etc) in thin films starting from the Langevin equation for the defect motion. We demonstrate that dynamical correlation functions $F_{2n}$ of vorticity and disclinicity behave as $F_{2n}\sim y^2/r^{4n}$ where $r$ is the characteristic scale and $y$ is the fugacity. As a consequence, below the Berezinskii-Kosterlitz-Thouless transition temperature $F_{2n}$ are characterized by anomalous scaling exponents. The behavior strongly differs from the normal law $F_{2n}\sim F_2^n$ occurring for simultaneous correlation functions, the non-simultaneous correlation functions appear to be much larger. The phenomenon resembles intermittency in turbulence.

30 pages, 11 figures

References in corpus (2)

• Inverse versus direct cascades in turbulent advection
• Inverse cascade and intermittency of passive scalar in 1d smooth flow

Cited by in corpus (2)

• Motion, creation and annihilation of disclinations in multi-domain structured nematic liquid crystal cells
• Comment on "Probing vortex unbinding via dipole fluctuations"