Speaker
Description
Thermalization is intimately connected to ergodicity in Hilbert space, namely the spreading of the wave function over the many-body Fock space, which links quantum dynamics to random matrix theory.
First, I will discuss the self-dual kicked Ising model, a minimal model of many-body quantum chaos, and show how an initially localized state converges to a Haar-random state with Porter–Thomas statistics. Second, I will show that entanglement entropies can be fully ergodic even when the wave function occupies only a vanishing fraction of the Hilbert space.
Finally, I will ask whether ergodicity can be defined independently of the observable. Using quantum k-designs and their frame potential, I will show that fractal states look Haar-random at the level of k moments only when their fractal dimension is large enough.