Normal Typicality and Dynamical Typicality for a Random Block-Band Matrix Model

par Cornelia Vogel (Ludwig Maximilian University of Munich)

mardi 24 mars 2026, 09:50 → 10:50 Europe/Paris

Amphi Schwartz

We consider a closed macroscopic quantum system in a pure state evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces (''macro spaces'') of the system's (high-dimensional) Hilbert space. We are interested in what the time evolution of the system's wave function looks like macroscopically, in particular, how much of it lies in a certain macro space. Two important related phenomena are the ones of normal typicality (a type of long-time behavior) and dynamical typicality (a type of similarity of the time evolution for initial states from a certain macro space). Here, we prove normal as well as dynamical typicality for a (centered) random block-band matrix model with block-dependent variances. A key feature of our model is that we achieve intermediate equilibration times, an aspect that has not been proven rigorously in any model before. Our proof builds on recently established concentration estimates for products of resolvents of Wigner-type random matrices and an intricate analysis of the deterministic approximation. This talk is based on joint work with László Erdős, Joscha Henheik, Stefan Teufel and Roderich Tumulka.