Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives

Abstract

Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates which precludes exploration of the full Hilbert space. However, we find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity -- generated by the Fibonacci word and its generalizations -- for which CHSE can be proven to occur. Our results provide a basis for understanding thermalization in general time-dependent quantum systems.

6 pages, 3 figures (main text); 14 pages, 3 figures (supplemental material)

References in corpus (1)

• Thermalization and its mechanism for generic isolated quantum systems

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