Examples for stable quantum currents

TL;DR

This paper mathematically analyzes two models, the 2D spin-1/2 Quantum Walk and Kagome quantum network, to demonstrate stable quantum currents and the underlying spectral theory.

Contribution

It provides a rigorous mathematical framework for understanding stable quantum currents in these models, linking them to the theory of absolutely continuous spectrum.

Findings

Demonstrates stable quantum currents in the models

Connects the models to the theory of stable absolutely continuous spectrum

Provides mathematical validation for phenomena observed in condensed matter experiments

Abstract

We provide a mathematical analysis of two models advocated in the theoretical and experimental condensed matter literature: the two dimensional spin-$1/2$ Quantum Walk and the Kagome quantum network; they apply to occurrence of stable quantum currents. This illustrates the theory of stable absolutely continuous spectrum and stable currents developed in \cite{ABJ5}.