Quantum $RLC$ circuits: charge discreteness and resonance

TL;DR

This paper applies a semiclassical quantum circuit theory to analyze charge discreteness and resistance effects in RLC circuits, deriving energy spectra and resonance behaviors with nonlinear considerations.

Contribution

It introduces new applications of the semiclassical quantum circuit theory to RLC circuits, including energy level calculations and resonance analysis with charge discreteness and resistance.

Findings

Derived Stark ladder energies for zero resistance circuits.

Generalized results for circuits driven by combined d.c. and a.c. emf.

Analyzed the impact of resistance and charge discreteness on resonance and nonlinear effects.

Abstract

In a recent article, we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance, inductive circuit, we obtain the Stark ladder energies in yet another way; and generalize earlier results by Chandia et. al, for the circuit driven by a combination d.c. plus a.c. electromotive force (emf). As a second application, we investigate the effect of electrical resistance, together with charge discreteness, in the current amplitude, and resonance conditions of a general $RLC$ quantum circuit, including nonlinear effects up to third order on the external sinusoidal emf.