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

Abstract

We prove normal typicality and 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 [arXiv:2403.10359] and an intricate analysis of the deterministic approximation.

23 pages LaTeX, 2 figures; v2: minor improvements throughout the paper; final version

References in corpus (16)

• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Quantum equilibration in finite time
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Dynamical typicality of quantum expectation values
• On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
• Normal Typicality and von Neumann's Quantum Ergodic Theorem
• On the time scales in the approach to equilibrium of macroscopic quantum systems
• Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace
• Quadratic vector equations on complex upper half-plane
• Dynamical typicality of isolated many-body quantum systems
• Concentration of measure for quantum states with a fixed expectation value
• Why are macroscopic experiments reproducible? Imitating the behavior of an ensemble by single pure states
• Dynamical typicality approach to eigenstate thermalization
• Time Evolution of Typical Pure States from a Macroscopic Hilbert Subspace
• Typical Macroscopic Long-Time Behavior for Random Hamiltonians
• Prethermalization for Deformed Wigner Matrices