Signed zeroes of Gaussian vector fields–Density, correlation functions and curvature
نویسنده
چکیده
Abstract. We calculate correlation functions of the (charge) density of zeroes of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one and two point functions. The zeroes of a two dimensional Gaussian vector field model the distribution of topological defects in the high temperature phase of two dimensional systems with orientational degrees of freedom, such as superfluid films, thin superconductors and liquid crystals.
منابع مشابه
Signed zeros of Gaussian vector fields–density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of Gaussian distributed vector fields. We are able to express correlation functions of arbitrary order through the curvature tensor of a certain abstract Riemann Cartan or Riemannian manifold. As an application, we discuss one and twopoint functions. The zeros of a two-dimensional Gaussian vector field model the distribution of...
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