Coherent transport over an explosive percolation lattice
Yalçınkaya, İskender and Gedik, Zafer (2017) Coherent transport over an explosive percolation lattice. Journal of Physics A: Mathematical and Theoretical, 50 (15). ISSN 1751-8113 (Print) 1751-8121 (Online)
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Official URL: http://dx.doi.org/10.1088/1751-8121/aa6201
We investigate coherent transport over a finite square lattice in which the growth of bond percolation clusters are subjected to an Achlioptas type selection process, i.e., whether a bond will be placed or not depends on the sizes of clusters it may potentially connect. Different than the standard percolation where the growth of discrete clusters are completely random, clusters in this case grow in correlation with one another. We show that certain values of correlation strength, if chosen in a way to suppress the growth of the largest cluster which actually results in an explosive growth later on, may lead to more efficient transports than in the case of standard percolation, satisfied that certain fraction of total possible bonds are present in the lattice. In this case transport efficiency obeys a power law in the vicinity of bond fraction where effective transport begins. It turns out that the higher correlation strengths may also reduce the efficiency as well. We also compare our results with those of the incoherent transport and examine the spreading of eigenstates of corresponing structures. We demonstrate that structural differences of discrete clusters due to different correlations result in different localization properties.
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