Oliver Lunt

Emergent random matrix universality in quantum operator dynamics

The memory function description of many-body quantum operator dynamics involves a carefully chosen split into ‘fast’ and ‘slow’ modes. An approximate model for the fast modes can then be used to solve for Green’s functions of the slow modes.

Using a formulation in operator Krylov space, we prove the emergence of a universal random matrix description of the fast mode dynamics. This emergent universality can occur in both chaotic and non-chaotic systems, provided their spectral functions are sufficiently smooth. Our proof involves a map to a Riemann-Hilbert problem which we solve using a nonlinear steepest-descent-type method. We discuss how a recent conjecture from quantum chaos, the 'Operator Growth Hypothesis', implies that chaotic operator dynamics can generically be identified with the critical point of a confinement transition in a classical Coulomb gas. We further use these results to develop a new numerical approach for estimating spectral functions.