Coherent dynamics on hierarchical systems

Alexander Blumen, Veronika Bierbaum and Oliver Mülken

Physica A: Statistical Mechanics and its Applications, 2006, vol. 371, issue 1, 10-15

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⩽21, 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.

Keywords: Random walks; Quantum walks; Exciton transport; Hyperbranched macromolecules; Dendrimers; Husimi cactus (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:371:y:2006:i:1:p:10-15

DOI: 10.1016/j.physa.2006.04.078

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