Evaluation of Spectral Zeta-Functions with the Renormalization Group

TL;DR

This paper evaluates spectral zeta-functions of specific network Laplacians using the renormalization group, focusing on Hanoi and hierarchical networks, with applications in quantum search and synchronization.

Contribution

It introduces exact evaluation methods for spectral zeta-functions of certain networks via the renormalization group, expanding analytical tools for complex network analysis.

Findings

Exact spectral zeta-functions computed for Hanoi and hierarchical networks.

Potential applications demonstrated in quantum search algorithms.

Insights into synchronization phenomena in complex networks.

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.