Transport properties in directed Quantum Walks on the line

TL;DR

This paper derives analytical expressions for the transport properties of directed continuous-time quantum walks on an infinite line, revealing how phase adjustments influence decay rates and showing certain statistical properties are direction-independent.

Contribution

It provides the first analytical formulas for directed quantum walks on a line, expanding previous results and exploring the effects of phase adjustments on transport dynamics.

Findings

Normal and enhanced decay rates can be achieved by phase tuning.

Mean and standard deviation are direction-independent for specific initial conditions.

Analytical expressions for probability distributions are derived.

Abstract

We obtained analytical expressions considering a directed continuous-time quantum walk on a directed infinite line using Bessel functions, expanding previous results in the literature, for a general initial condition. We derive the equation for the probability distribution, and show how to recover normal and enhanced decay rates for the survival probability by adjusting the phase factor of the direction of the graph. Our result shows that the mean and standard deviation for a specific non-local initial condition does not depend on the direction.