Evaluation of Spectral Zeta-Functions with the Renormalization Group
arXiv:1607.05168 · doi:10.1088/1751-8121/aa5c09
Abstract
We evaluate spectral zeta-functions of certain network Laplacians that can be treated exactly with the renormalization group. As specific examples we consider a class of Hanoi networks and those hierarchical networks obtained by the Migdal-Kadanoff bond moving scheme from regular lattices. As possible applications of these results we mention quantum search algorithms as well as synchronization, which we discuss in more detail.
24 pages, 7 figures, numerous updates