Sprecher
Beschreibung
Thermalization is deeply connected to the notion of ergodicity in Hilbert space, implying the equipartition of the wave function over the available many-body Fock states. Under unitary time evolution, an initially structured state spreads in Fock space, approaching a Haar-random state, thereby revealing a deep connection between many-body quantum systems and random matrix theory.
In the first part of this talk, I will discuss the dynamics of the self-dual kicked Ising model, a minimal model of many-body quantum chaos that is unitary in both time and space. I will focus on its evolution in Fock space, showing how the probability distribution of the initial state approaches that of a random state, characterized by the Porter-Thomas distribution.
In the second part, I will explore general relationships between entanglement and the spread of the wave function in Fock space. I will demonstrate that entanglement entropies can still exhibit fully ergodic behavior, even when the wave function occupies only a vanishing fraction of the full Hilbert space in the thermodynamic limit.
