Coherent dynamics on hierarchical systems

Details Coherent dynamics on hierarchical systems Coherent dynamics on hierarchical systems

2006-10-25

arxiv.org/abs/cond-mat/0610686v1

Physica A 371, 10 (2006)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 5 figures

Scientific paper

10.1016/j.physa.2006.04.078

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.

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