Resonant frequencies and spatial correlations in frustrated arrays of Josephson type nonlinear oscillators

TL;DR

This paper theoretically investigates resonant frequencies and spatial phase correlations in frustrated Josephson junction arrays, revealing a transition from long- to short-range correlations at a critical frustration level and confirming findings with Monte Carlo simulations.

Contribution

It introduces a detailed analysis of phase dynamics and correlations in frustrated Josephson arrays, highlighting the impact of frustration on spatial correlations and dispersion relations.

Findings

Identification of multiband dispersion relations in arrays

Transition from long- to short-range correlations at critical frustration

Higher-order correlations restore long-range behavior near full frustration

Abstract

We present a theoretical study of resonant frequencies and spatial correlations of Josephson phases in frustrated arrays of Josephson junctions. Two types of one-dimensional arrays, namely, the diamond and sawtooth chains, are discussed. For these arrays in the linear regime the Josephson phase dynamics is characterized by multiband dispersion relation $\omega(k)$, and the lowest band becomes completely $flat$ at a critical value of frustration, $f=f_c$ . In a strongly nonlinear regime such critical value of frustration determines the crossover from non-frustrated ($0<f<f_c$) to frustrated ($f_c<f<1$) regimes. The crossover is characterized by the thermodynamic spatial correlation functions of phases on vertices, $\varphi_i$, i.e. $C_p(i-j)=\langle\cos[p(\varphi_i - \varphi_j)]\rangle$ displaying the transition from long- to short-range spatial correlations. We find that higher-order correlations functions, e.g. $p=2$ and $p=3$, restore the long-range behavior deeply in the frustrated regime, $f\simeq 1$. Monte-Carlo simulations of the thermodynamics of frustrated arrays of Josephson junctions are in good agreement with analytical results.