Intermittency in Dynamics of Two-Dimensional Vortex-like Defects

TL;DR

This paper investigates the complex, scale-dependent behavior of vortex-like defects in thin films, revealing anomalous scaling and intermittency phenomena akin to turbulence, especially below the BKT transition.

Contribution

It introduces a detailed analysis of high-order defect correlations, demonstrating their anomalous scaling and intermittency, which differ from traditional correlation behaviors.

Findings

High-order correlation functions scale as $F_{2n} o y^2/r^{4n}$.

Below BKT transition, correlations exhibit anomalous scaling exponents.

Non-simultaneous correlations are significantly larger than expected from normal laws.

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.