Energy spectrum of the quantum vortices configurations

Abstract

A review of various exactly solvable models on the determination of the energy spectra E (k) of 3D-velocity field, induced by chaotic vortex lines is proposed. This problem is closely related to the sacramental question whether a chaotic set of vortex filaments can mimic the real hydrodynamic turbulence [1]. The quantity v(k)v(-k) can be exactly calculated, provided that we know the probability distribution functional P({s(\xi ,t)}) of vortex loops configurations