Coherent dynamics on hierarchical systems

TL;DR

This paper investigates quantum transport on hierarchical Husimi cactus structures, revealing initial site dependence, recurrence properties, and characteristic probability patterns through quantum walks.

Contribution

It introduces analysis of quantum walks on Husimi cacti, highlighting initial site effects and establishing bounds for return probabilities, a novel approach for hierarchical systems.

Findings

Transport depends on initial excitation site.

Central sites exhibit near recurrence for small systems.

Characteristic probability patterns distinguish quantum from classical behavior.

Abstract

We study the coherent transport modeled by continuous-time quantum walks, focussing on hierarchical structures. For these we use Husimi cacti, lattices dual to the dendrimers. We find that the transport depends strongly on the initial site of the excitation. For systems of sizes $N\le21$, we find that processes which start at central sites are nearly recurrent. Furthermore, we compare the classical limiting probability distribution to the long time average of the quantum mechanical transition probability which shows characteristic patterns. We succeed in finding a good lower bound for the (space) average of the quantum mechanical probability to be still or again at the initial site.