Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1998-12-07
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
15 pages, 2 figures, to appear in the Proceedings of the Conference "Macroscopic Quantum Tunneling and Coherence", Napoli (I),
Scientific paper
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.
Falci Giuseppe
Weiss Ulrich
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