Quantum LC circuits with charge discreteness: normal and anomalous spectrum

TL;DR

This paper analyzes a quantum LC circuit considering charge discreteness, revealing two spectral branches: a normal one with integer effective charge and an anomalous one with non-integer effective charge, with potential implications for mesoscopic systems.

Contribution

It introduces a solvable model of a quantum LC circuit with charge discreteness, identifying normal and anomalous spectral branches and their characteristics.

Findings

Normal branch with integer effective charge spectrum

Anomalous branch with non-integer effective charge spectrum

Estimated non-integer charge parameter x~0.7 for mesoscopic data

Abstract

A solvable quantum $LC$ circuit with charge discreteness is studied. Two discrete spectral branches are obtained: (i) the normal branch corresponding to a charged capacitor with integer effective charge $k=q_{e}n$ ($q_{e}$ elementary charge, $n$ integer) and (ii) the anomalous branch where the energy is related to non-integer effective charge $k=q_{e}(n-x)$ in the capacitor. For usual mesoscopics data like quantum point contact we found $x\sim 0.7$.