Many-body quantum chaos exhibits many interesting features at different time scales. Before and around scrambling time, it has a significant exponential growth in four-point out-of-time-ordered correlators. This exponential growth speed is called quantum Lyapunov exponent that has been shown to be bounded by 2\pi T. Maximal chaos is referred to as the bound saturated. It is well-known that the Schwarzian can be regarded as an effective theory for maximal chaos in 0+1 dimension. This corresponds to the near horizon graviton-exchange scattering in 1+1 dimensional AdS black hole. More generally, it can be described by an effective theory with appropriate shift symmetry. In this talk, I will propose a new effective theory for non-maximal chaotic systems, in which we introduce two effective modes and a generalized shift symmetry. This formalism can explain the non-maximal chaos in large q SYK model and can also reproduce the scattering formula near the AdS_2 black hole horizon with stringy correction. Some future directions will be discussed if time permits.
Bibliography：Ping Gao, MIT
Ping Gao earned Ph.D. from Harvard University in 2019 and now is a postdoc at the Center for Theoretical Physics of MIT. His interest includes holographic duality, quantum gravity, quantum information, quantum chaos, SYK model, and effective theory for hydrodynamics.
Zoom Meeting:
https://cern.zoom.us/j/96357968034?pwd=K2REeGF0V2dqOElRd09hVGVRcDk4Zz09
Zoom：963 5796 8034
pwd：125125
Prof. Yinan Wang