Josephson Junctions and AdS/CFT Networks

TL;DR

This paper introduces a holographic model of Josephson junctions using multi-gravity theories on AdS spacetimes, revealing complex superconducting behaviors and new equations generalizing the Gross-Pitaevskii equation.

Contribution

It develops a novel holographic framework for Josephson junctions and networks, connecting multi-gravity theories with complex superconducting phenomena.

Findings

Demonstrates a Josephson junction model with the sine current-phase relation.

Finds that Cooper-pair condensates in chains obey a discretized Schrödinger-type equation.

Reveals complex behaviors including chaos, solitons, and modulated superconductivity in the model.

Abstract

We propose a new holographic model of Josephson junctions (and networks thereof) based on designer multi-gravity, namely multi-(super)gravity theories on products of distinct asymptotically AdS spacetimes coupled by mixed boundary conditions. We present a simple model of a Josephson junction (JJ) that exhibits the well-known current-phase sine relation of JJs. In one-dimensional chains of holographic superconductors we find that the Cooper-pair condensates are described by a discretized Schrodinger-type equation. Such non-integrable equations, which have been studied extensively in the past in condensed matter and optics applications, are known to exhibit complex behavior that includes periodic and quasiperiodic solutions, chaotic dynamics, soliton and kink solutions. In our setup these solutions translate to holographic configurations of strongly-coupled superconductors in networks with weak site-to-site interactions that exhibit interesting patterns of modulated superconductivity. In a continuum limit our equations reduce to generalizations of the Gross-Pitaevskii equation. We comment on the many possible extensions and applications of this new approach.