110 research outputs found
Coherent exciton transport in dendrimers and continuous-time quantum walks
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.Comment: 8 pages, 8 figures, accepted for publication in J. Chem. Phy
Slow Encounters of Particle Pairs in Branched Structures
On infinite homogeneous structures, two random walkers meet with certainty if
and only if the structure is recurrent, i.e., a single random walker returns to
its starting point with probability 1. However, on general inhomogeneous
structures this property does not hold and, although a single random walker
will certainly return to its starting point, two moving particles may never
meet. This striking property has been shown to hold, for instance, on infinite
combs. Due to the huge variety of natural phenomena which can be modeled in
terms of encounters between two (or more) particles diffusing in comb-like
structures, it is fundamental to investigate if and, if so, to what extent
similar effects may take place in finite structures. By means of numerical
simulations we evidence that, indeed, even on finite structures, the
topological inhomogeneity can qualitatively affect the two-particle problem. In
particular, the mean encounter time can be polynomially larger than the time
expected from the related one particle problem.Comment: 8 pages, 12 figures; accepted for publication in Physical Review
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