Title: The Spectral Form Factor: From Hydrodynamics to the Riemann Zeta Function
Abstract: We discuss two aspects of the spectral statistics of chaotic systems. First we discuss how the Spectral Form Factor captures the system's thermal relaxation, and how a quantitative study of these effects gives rise to a novel theory similar to (but not the same as) fluctuating hydrodynamics. Then we will turn our attention to long times, where we find a surprising resurgence of this early-time relaxation phenomenon around the Poincare recurrence time. We show that this follows from the Riemann-Siegel lookalike formula, a spectral statistics theorem inspired by work on the Riemann zeta function.
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