On December 22 at 6:30 PM, Daniil Kochergin will give a talk titled "Anderson Localization on Graphs with Chiral and Bogoliubov-de Gennes Symmetry Classes."
Abstract: Single-particle localization on graphs is most often studied using graph ensembles, which are a subclass of Gaussian ensembles. In this talk, I will discuss the localization effects that arise when the adjacency matrix of a graph in an ensemble has a chiral or Bogoliubov-de Gennes symmetry class. For such ensembles, the density of states, the distance between nearest energy levels, and the fractal dimension were studied as a function of the magnitude of diagonal disorder. The fractal dimension revealed zero-mode effects in chiral models. For graphs with the Bogoliubov-de Gennes class, there are significant differences between the symmetry-preserving and symmetry-breaking disorders. The transition from a model with multiparticle localization to a single-particle model with the Bogolyubov-de Gennes class will be considered. Based on the paper https://arxiv.org/abs/2510.10255