Coherent dynamics on hierarchical systems

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 $N\le 21$, 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.

7 pages, 5 figures

References in corpus (6)

• Quantum Computation and Decision Trees
• Coherent exciton transport in dendrimers and continuous-time quantum walks
• Spacetime structures of continuous time quantum walks
• Slow transport by continuous time quantum walks
• Asymmetries in symmetric quantum walks on two-dimensional networks
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• Transport efficiency of continuous-time quantum walks on graphs
• Swift chiral quantum walks
• Topology and energy transport in networks of interacting photosynthetic complexes
• Coherent transport over an explosive percolation lattice
• Perturbed graphs achieve unit transport efficiency without environmental noise