Coherent exciton transport in dendrimers and continuous-time quantum walks

TL;DR

This paper investigates coherent exciton transport in dendrimers using continuous-time quantum walks, revealing perfect recurrences in small dendrimers and complex transport patterns in larger ones, with implications for understanding quantum transport phenomena.

Contribution

It introduces a quantum walk model for exciton transport in dendrimers and analyzes how size and initial conditions affect transport efficiency and recurrence.

Findings

Perfect recurrences in small dendrimers when starting at the center

Transport to certain nodes is very low depending on initial site

A lower bound for return probability based on eigenvalues

Abstract

We model coherent exciton transport in dendrimers by continuous-time quantum walks (CTQWs). For dendrimers up to the second generation the coherent transport shows perfect recurrences, when the initial excitation starts at the central node. For larger dendrimers, the recurrence ceases to be perfect, a fact which resembles results for discrete quantum carpets. Moreover, depending on the initial excitation site we find that the coherent transport to certain nodes of the dendrimer has a very low probability. When the initial excitation starts from the central node, the problem can be mapped onto a line which simplifies the computational effort. Furthermore, the long time average of the quantum mechanical transition probabilities between pairs of nodes show characteristic patterns and allow to classify the nodes into clusters with identical limiting probabilities. For the (space) average of the quantum mechanical probability to be still or again at the initial site, we obtain, based on the Cauchy-Schwarz inequality, a simple lower bound which depends only on the eigenvalue spectrum of the Hamiltonian.