Quantum circuits under magnetic field

TL;DR

This paper investigates the effects of a constant magnetic flux on a quantum LC circuit by deriving a new Schrödinger equation form, analyzing the energy spectrum differences from previous models, and highlighting potential experimental distinguishability.

Contribution

The paper introduces a new potential form for the quantum LC circuit under magnetic flux and compares its energy spectrum with previous models, revealing significant differences.

Findings

Different energy spectra from the new and previous models

Spectral differences vary with magnetic flux

Potential for experimental distinction between models

Abstract

We consider a quantum $LC$ circuit under a constant magnetic flux $f$, and derive a discretized form of the Schr\"odinger equation, which is equivalent to introducing a {\em potential} $V(\phi,f)$ in the pseudo-flux $\phi$-representation, which is different from that found previously by Li and Chen \cite{LI-CHEN}. Firts, we discuss the physical assumptions leading to these different results, and then study the energy spectrum of the $LC$ quantum circuit as a function of a constant external magnetic flux, using a direct numerical approach. The results are compared with the spectrum obtained using the Li-Chen potential. Our results indicate that the energy spectra from both models are quite different numerically, and as a function of $f$, so that they may be clearly distinguished under appropiate experimental conditions.