Thermal fluctuations of the Josephson current in a ring of superconducting grains

TL;DR

This paper investigates thermal fluctuations of the Josephson current in a superconducting ring, introducing a new numerical method and analyzing transition rates and current behavior under different flux conditions.

Contribution

It presents a novel numerical approach to study both equilibrium and dynamic properties of Josephson systems, with analytical and numerical analysis of phase slip effects.

Findings

Transition rate follows an Arrhenius form with size-dependent parameters.

At half-fluxon, current exhibits incoherent transitions due to thermal phase slips.

At quarter-fluxon, the current decreases with temperature and is affected by phase slips.

Abstract

Thermal fluctuations of the Josephson current $I$ induced by the magnetic flux through a ring of $N$ superconducting grains are studied. When a half-fluxon is threading the ring, $I$ exhibits incoherent transitions between the two degenerate states due to thermal phase slips. We propose a new numerical method to deal with both equilibrium and dynamic properties of Josephson systems. Computed transition rate has the form $\Gamma = A(N)\exp[-B(N)/T]$, where $B(N)$ agrees with the analytical result derived for the energy barrier associated with phase slips. In the non-degenerate case (e.g., at a quarter-fluxon) the equilibrium value of $I$ decreases with $T$ due to harmonic excitations and then gets destroyed by phase slips.