Duality in the Quantum Dissipative Villain Model and application to Mesoscopic Josephson Junction Circuits
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 (onedimensional Coulomb gases or surface roughening models) which are exactly selfdual. 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.
 Publication:

arXiv eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.condmat/9812101
 arXiv:
 arXiv:condmat/9812101
 Bibcode:
 1998cond.mat.12101F
 Keywords:

 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Superconductivity
 EPrint:
 15 pages, 2 figures, to appear in the Proceedings of the Conference "Macroscopic Quantum Tunneling and Coherence", Napoli (I), June 1998, Journal of Superconductivity (1999)