Disorder in the Sachdev–Ye–Kitaev model

Abstract

We give qualitative arguments in support of the mesoscopic nature of the Sachdev–Ye–Kitaev (SYK) model in the regime with q2/N≪1 with N Majorana particles coupled by antisymmetric and random interactions of range q. Using a stochastic deformation of the SYK model, we show that its characteristic determinant obeys a viscid Burgers equation with a small spectral viscosity in the regime with q/N=1/2. In particular, the stochastic evolution of the SYK model can be mapped exactly onto that of random matrix theory, with universal Airy oscillations at the edges.