Seminario di Gruppo IV

We compare and contrast the Random Matrix Theory (RMT) properties of various SYK-like hamiltonians: the Gurau-Witten (GW) model, the standard SYK model and a flavored version of the SYK model due to Gross and Rosenhaus. The latter, even though disorder averaged, shows parallels with the GW model. In particular, the two models fall into identical Andreev ensembles as a function of N. Our main diagnostic tool of the chaos aspects of these models is the Spectral Form Factor (SFF). We relate the main features and peculiarities of the SFF with the features of the spectra of the corresponding hamiltonians. We also provide estimates of the relevant time scales of a given model on the base of the corresponding spectrum.