Orateur
Description
Ergodicity in quantum systems is often defined through statistical properties of energy eigenstates, such as Berry's conjecture for single particle chaotic systems, and the eigenstate thermalization hypothesis (ETH) for many-body systems. In this talk, I would like to pose the question whether there are quantum systems which can exhibit a stronger form of ergodicity, namely whether dynamics is such that any time-evolved state visits every point in Hilbert space uniformly over time. We call such a phenomenon Complete Hilbert Space Ergodicity (CSHE), and it represents a notion of ergodicity more akin to the intuitive notion of ergodicity as an inherently dynamical concept, i.e., that a system eventually explores all of its allowed 'phase space'. Naturally, CSHE cannot hold for systems which are time-independent or even time-periodic (owing to the existence of energy eigenstates which precludes exploration of the full Hilbert space), but I will show that there exists a family of simple, aperiodic, yet deterministic driving protocols --- drives generated by the Fibonacci word and its generalizations --- for which CQE can be proven to occur. Our results provide a basis toward understanding how thermalization arises in general time-dependent quantum many-body systems, and in fact implies a more stringent form of local equilibration called deep thermalization.
