Time: 2:30-4:00    July 1, 2, 3,  2019 

Abstract:  

Out-of-time-order  correlators (OTOCs) are a diagnostic of chaos in quantum many-body systems.  Although OTOCs are hard to measure experimentally, they may be computed  efficiently in models with a large parameter N (for systems with all-to-all  interactions, N is simply the number of degrees of freedom). In these lectures,  I will explain the retarded kernel method that is often used to compute the  early-time OTOCs in SYK-like models. Within the framework, one can further  define a time scale called the "branching time". In the near-maximal chaos, the  branching time characterizes the "incoherence" in the scrambling. I will derive  an identity relating the growth exponent (i.e., the Lyapunov exponent), the  pre-exponential factor and the branching time. The identity has multiple  applications. As a somewhat mysterious application, I will show that exact  maximal chaos could occur in the butterfly wavefront of an SYK-like  one-dimensional model.

The lectures are  based on [arXiv: 1812.00120].