In this talk, we investigate the behavior of purity and out-of-time-ordered correlations in random quantum circuits. We show that the time evolution of both quantities can be described by a Markov chain, and their relaxation towards their asymptotic values is not governed by the second largest eigenvalue of the transfer matrix, as one could expect. The exponential relaxation is instead given by an “eigenvalue”, which is not in the spectrum of the transfer matrix at all — a phantom eigenvalue. We shall explore this phenomenon and find that it is rooted in the non-Hermiticity of the transfer matrix and in the locality of the dynamics.

*Jaš Bensa: University of Ljubljana