Wavefront solution in extended quantum circuits with charge discreteness

TL;DR

This paper introduces a wavefront solution for quantum transmission lines with charge discreteness, revealing how nonlinearity and flux discontinuities influence wavefront velocity and stability, and connecting the model to the quantum Toda lattice.

Contribution

It presents the first wavefront solution in extended quantum circuits with charge discreteness, linking nonlinearity to charge effects and establishing a connection with the quantum Toda lattice.

Findings

Wavefront velocity depends on flux discontinuities with allowed and forbidden regions.

Preliminary stability analysis of the wavefront solutions is provided.

Connection established between the quantum transmission line model and the quantum Toda lattice.

Abstract

A wavefront solution for quantum (capacitively coupled) transmission lines with charge discreteness (PRB {\bf 64}, 235309 (2001)) is proposed for the first time. The nonlinearity of the system becomes deeply related to charge discreteness. The wavefront velocity is found to depend on a step discontinuity on the (pseudo) flux variable, $f$, displaying allowed and forbidden regions (gaps), as a function of $f$. A preliminary study of the stability of the solutions is presented. The dual transmission line hamiltonian is proposed and finally, we find a connection with the (quantum) Toda lattice.