Thermalization slowing down in multidimensional Josephson junction networks

TL;DR

This paper investigates how thermalization slows down in multidimensional Josephson junction networks by analyzing their Lyapunov spectra, revealing two universality classes governed by the ratio of Josephson coupling to energy density.

Contribution

It identifies two universality classes of thermalization slowing-down in Josephson networks and characterizes their divergence behavior across dimensions using Lyapunov spectrum analysis.

Findings

Two universality classes of thermalization slowing-down identified.

Weak-coupling regime allows chaos with near-conserved quantities.

Universal critical exponents characterize the weak-coupling class.

Abstract

We characterize thermalization slowing-down of Josephson junction networks in 1, 2 and 3 spatial dimensions for systems with hundreds of sites by computing their entire Lyapunov spectra. The ratio of Josephson coupling $E_J$ to energy density $h$ controls two different universality classes of thermalization slowing-down, namely the weak coupling regime, $E_J/h \rightarrow 0$, and the strong coupling regime, $E_J/h \rightarrow \infty$. We analyze the Lyapunov spectrum by measuring the largest Lyapunov exponent and by fitting the rescaled spectrum with a general ansatz. We then extract two scales: the Lyapunov time (inverse of the largest exponent) and the exponent for the decay of the rescaled spectrum. The two universality classes, which exist irrespective of network dimension, are characterized by different ways the extracted scales diverge. The universality class corresponding to the weak-coupling regime allows for the coexistence of chaos with a large number of near-conserved quantities and is shown to be characterized by universal critical exponents, in contrast with the strong-coupling regime. We expect our findings, which we explain using perturbation theory arguments, to be a general feature of diverse Hamiltonian systems.