Analytical Description of the Quantum-Mesoscopic-Classical Transition in Systems with Quasi-Discrete Environment

TL;DR

This paper presents an analytical framework using matrix theta-functions to describe the quantum to classical transition in transport properties of nano-materials with quasi-discrete environments, relevant for Josephson junctions and granular systems.

Contribution

It introduces a novel analytical method to model the quantum-classical transition in systems with discrete environmental spectra, advancing understanding of transport phenomena.

Findings

Analytical expression for transport characteristics across temperature regimes

Captures the quantum to classical transition in nano-materials

Applicable to Josephson junction arrays and granular systems

Abstract

We investigate dynamic properties of inhomogeneous nano-materials, which appear in analytical descriptions typically as series of $\delta$-functions with corresponding Gibbs weights. We focus on observables relevant for transport theories of Josephson junction arrays and granular systems near the superconductor -- insulator transition. Furthermore, our description applies to the theory of tunnel junctions exchanging energy with a "bath", the latter having a discrete spectrum. Using the matrix theta-function formalism we find an analytical expression for the transport characteristics capturing the complete temperature driven transition from the quantum to the classical regime.