Localization in hierarchical networks: From statistical physics to neuroscience and materials science applications



Paolo Moretti

19. November 2019, 17.00
WW8, Raum 2.018, Dr.-Mack-Str. 77, Fürth


Graphs, or networks, are commonly employed to model complex adjacency patterns in the biophysical realm, as well as in techno-social applications. Even in the most common case of classical dynamics, networks can host localization phenomena. Here localization should be understood as the emergence of localized eigenvectors in the matrices encoding the network connectivity patterns (adjacency matrices, discrete Laplace operators, etc.). As in the quantum case, network localization often ensues in low dimensional systems, where the concept of "absence of diffusion" becomes "critical slowing down". This the case of hierarchical networks, which are commonly used to model biological systems. Transport in hierarchical networks is known to generate Griffiths phases, extended regions in parameter space, associated with scale invariant behaviour and anomalously slow dynamics. I will review some of my recent results in this field, presenting the general theoretical underpinnings and some selected applications in the fields of brain dynamics and material deformation.