Kadanoff Seminar -  Hydrodynamics and the Spectral Form Factor, Brian Swingle, University of Maryland

Hydrodynamics and the Spectral Form Factor, Brian Swingle, University of Maryland

Ensembles of quantum chaotic systems are expected to exhibit random matrix universality in their energy spectrum. The presence of this universality can be diagnosed by looking for a linear in time 'ramp' in the spectral form factor, but for realistic systems this feature is typically only visible after a sufficiently long time. I will discuss several developments in our understanding of this intermediate time regime in the spectral form factor. First, I will describe a hybrid system in which the single particle levels are chaotic while the many-body levels are those of non-interacting particles. In this case, the linear ramp is replaced by an exponential ramp. Interacting deformations of the system can then lead to full many-body quantum chaos, but the approach to a linear ramp can be slow due to the presence of nearly conserved modes. Motivated by this problem, I will present a theory of the spectral form factor in systems with slow modes and will apply the results to a variety of hydrodynamic systems. Joint work with Mike Winer and Shaokai Jian.