The Quantum Dissipative Villain Model

TL;DR

The paper introduces the Quantum Dissipative Villain (QDV) model to study tunneling in dissipative quantum systems, revealing a rich dual structure and exact mappings across various representations, applicable to physical systems like Josephson junctions.

Contribution

It presents the QDV model with explicit discrete tunneling degrees of freedom, deriving exact dual mappings and equations, generalizing classical network analogies, and extending the Schmid self-duality to broader environments.

Findings

Derived exact mappings for the QDV model across dual representations

Established the self-dual structure for general linear environments

Connected the QDV model to physical systems like Josephson junctions

Abstract

We introduce the Quantum Dissipative Villain (QDV) model as a prototype model to study tunneling in dissipative quantum mechanics. Dissipation is provided by a coupled linear environment. In the QDV model, the discrete character of a tunneling degree of freedom coupled to an environment is explicit, leading to a rich dual structure. We derive general exact mappings of the QDV model on several dual discrete representations, including pairs of self-dual models, for general linear environments and arbitrary temperatures. Self-duality allows to write exact equations for each correlation function of each representation. Analogies with the theory of classical network transformations are also presented. Finally we discuss the fundamental character of the QDV model. For instance, the standard Caldeira-Leggett model, which describes mesoscopic Josephson junctions in a circuit and many other physical systems, is a special QDV model. The self-dual structure of the QDV model allows then the exact generalization of the Schmid approximate self-duality to general linear environments and arbitrary temperatures.