Quantum LC - circuits with diffusive modification of the continuity equation

TL;DR

This paper generalizes the quantum description of LC circuits by introducing a function F(n), leading to a modified continuity equation and site-dependent hopping amplitudes, supported by rational charge multiples.

Contribution

It presents a novel generalization of the quantum LC circuit model using an arbitrary integer-dependent function, resulting in diffusive continuity equation modifications.

Findings

Generalization of the discrete Schrödinger equation with F(n)

Derivation of site-dependent hopping amplitudes

Support for rational multiples of elementary charge

Abstract

Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n. Such generalization leads to site-dependent hopping amplitudes as well as to diffusive modification of the continuity equation. One shows, in particular, that there are firm supports concerning rational multiples of the elementary electric charge.