Exponential Suppression of Transport in Electric Quantum Walks

TL;DR

This paper proves that the maximum speed of quantum particles in electric fields decreases exponentially with field period, confirming a previous conjecture and providing exact relations and spectral characterizations.

Contribution

It establishes exact exponential decay of maximal group velocity in quantum walks under periodic electric fields, confirming and extending prior conjectures.

Findings

Maximal group velocity decays exponentially with field period

Explicit revival relations are demonstrated

Absolutely continuous spectrum is characterized

Abstract

We establish exact scalings for the maximal group velocity of translation-invariant quantum walks in periodic electric fields. Our main result shows that the maximal group velocity decays exponentially with the period of the field in the whole parameter range, thus affirming a conjecture of arXiv:2302.01869 and at the same time augmenting it to an exact equality. We further demonstrate explicit revival relations and characterize the absolutely continuous spectrum in these models. Our results apply directly also to generalized CMV matrices.