Numerical simulation of stochastic motion of vortex loops under action of random force. Evidence of the thermodynamic equilibrium

TL;DR

This paper uses numerical simulations to study the stochastic motion of vortex loops under random forces, demonstrating that the vortex system reaches thermodynamic equilibrium consistent with the fluctuation-dissipation theorem.

Contribution

It introduces a new algorithm for vortex reconnection and provides evidence that vortex tangles reach thermodynamic equilibrium in a stochastic model.

Findings

Vortex tangle reaches a stationary state with fluctuations.

The system attains thermodynamic equilibrium with temperature from fluctuation-dissipation theorem.

New vortex reconnection algorithm based on crossing lines.

Abstract

Numerical simulation of stochastic dynamics of vortex filaments under action of random (Langevin) force is fulfilled. Calculations are performed on base of the full Biot--Savart law for different intensities of the Langevin force. A new algorithm, which is based on consideration of crossing lines, is used for vortex reconnection procedure. After some transient period the vortex tangle develops into the stationary state characterizing by the developed fluctuations of various physical quantities, such as total length, energy etc. We tested this state to learn whether or not it the thermodynamic equilibrium is reached. With the use of a special treatment, so called method of weighted histograms, we process the distribution energy of the vortex system. The results obtained demonstrate that the thermodynamical equilibrium state with the temperature obtained from the fluctuation dissipation theorem is really reached. PACS-numbers: 67.40.Vs 98.80.Cq 7.37.+q