The Fibonacci quantum walk and its cassical trace map

TL;DR

This paper investigates a Fibonacci-structured quantum walk in momentum space, linking its sub-ballistic behavior to classical trace map correlations, and introduces a classical map model for this quantum system.

Contribution

It introduces a classical trace map model for the Fibonacci quantum walk, revealing the connection between quantum dynamics and classical correlation decay.

Findings

Quantum walk exhibits sub-ballistic spreading.

Power-law decay of correlations explains sub-ballistic behavior.

Classical trace map captures quantum dynamics features.

Abstract

We study the quantum walk in momentum space using a coin arranged in quasi-periodic sequences following a Fibonacci prescription. We build for this system a classical map based on the trace of the evolution operator. The sub-ballistic behavior of this quantum walk is connected with the power-law decay of the time correlations of the trace map.