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arXiv · 1801.03842

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

A. Andreanov·M. V. Fistul
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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.

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A. Andreanov, M. V. Fistul. 2018-01-11. Resonant frequencies and spatial correlations in frustrated arrays of Josephson type nonlinear oscillators. https://doi.org/10.1088/1751-8121%2Fab013d

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