Duality in the Quantum Dissipative Villain Model and application to Mesoscopic Josephson Junction Circuits

TL;DR

This paper introduces the Quantum Dissipative Villain Model to analyze self-duality in Josephson Junction circuits, providing exact mappings and impedance calculations for various environmental spectral densities and temperatures.

Contribution

It presents a novel exactly self-dual quantum model and applies duality to derive impedance expressions for Josephson Junction circuits under general conditions.

Findings

Exact self-duality in the Quantum Dissipative Villain Model

Derivation of impedance formulas for Josephson Junctions

Mapping of the model to Coulomb gases and surface roughening models

Abstract

We study exact self duality in the model of a Brownian particle in a washboard (WB) potential which describes a Josephson Junction (JJ) coupled to an environment, for arbitrary temperature and arbitrary form of the spectral density of the environment. To this end we introduce the Quantum Dissipative Villain Model (QDVM), which models tunneling of a degree of freedom coupled to a linear quantum environment through an infinite set of states. We derive general exact mappings on various dual discrete representations (one-dimensional Coulomb gases or surface roughening models) which are exactly self-dual. Then we show how the QDVM maps exactly onto the WB model and use duality relations to calculate the leading terms of the total impedance of a JJ circuit, for general frequency dependence of the spectral density of the environment and arbitrary temperature.