Applications of quantum integrable systems

TL;DR

This paper explores two novel applications of quantum integrable systems: generating high harmonics in solid state devices and modeling fractional quantum Hall conductance using affine Toda field theories.

Contribution

It introduces new methods to generate high harmonics and connect quantum wire conductance with fractional quantum Hall states through integrable models.

Findings

High harmonics can be generated from impurity quantum wires.

Conductance in quantum wires relates to Jain sequence filling fractions.

Quantum affine Toda theories model fractional quantum Hall effects.

Abstract

We present two applications of quantum integrable systems. First, we predict that it is possible to generate high harmonics from solid state devices by demostrating that the emission spectrum for a minimally coupled laser field of frequency $\omega$ to an impurity system of a quantum wire, contains multiples of the incoming frequency. Second, evaluating expressions for the conductance in the high temperature regime we show that the caracteristic filling fractions of the Jain sequence, which occur in the fractional quantum Hall effect, can be obtained from quantum wires which are described by minimal affine Toda field theories.