Disordered Josephson junction chains: Anderson localization of normal modes and impedance fluctuations

TL;DR

This paper investigates how disorder and absorption affect the normal modes and impedance of Josephson junction chains, revealing localization phenomena and impedance distribution characteristics.

Contribution

It provides a detailed analysis of mode localization and impedance fluctuations in disordered Josephson chains considering both disorder and absorption effects.

Findings

Localization length depends on disorder and absorption

Impedance distribution is Gaussian for long localization length

Impedance distribution has a power law tail in the opposite limit

Abstract

We study the properties of the normal modes of a chain of Josephson junctions in the simultaneous presence of disorder and absorption. We consider the superconducting regime of small phase fluctuations and focus on the case where the effects of disorder and absorption can be treated additively. We analyze the frequency shift and the localization length of the modes. We also calculate the distribution of the frequency-dependent impedance of the chain. The distribution is Gaussian if the localization length is long compared to the absorption length; it has a power law tail in the opposite limit.