Discrete-charge Quantum Circuits and Electrical Resistance

TL;DR

This paper explores quantum $LC$ and $RLC$ circuits with discrete charge, deriving energy eigenvalues and relating resistance to the Landauer formula, advancing understanding of quantum electrical systems.

Contribution

It introduces approximate energy eigenvalues for quantum $LC$ circuits with discrete charge and incorporates resistance, linking to the Landauer formula for the first time.

Findings

Derived approximate energy eigenvalues depending on charge quantization

Established a relation between quantum resistance and the Landauer formula

Extended classical quantum circuit theory to include resistance effects

Abstract

From the theory of quantum $LC$ circuits with discrete charge, and {\em semiclassical} considerations, we obtain approximate energy eigenvalues, depending on the parameter $q_e^2/h$. Next, we include electrical resistance for the quantum $RLC$ circuit, obtaining a relation that strongly reminds us of the Landauer formula.