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

We investigate dynamic properties of inhomogeneous nano-materials, which appear in analytical descriptions typically as series of $δ$-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.

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