Smooth Crossover Between Weak and Strong Thermalization using Rigorous Bounds on Equilibration of Isolated Systems
arXiv:2310.13392 · doi:10.1016/j.physa.2024.130065
Abstract
It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found and the phenomenon was named weak thermalization. Later, it was argued that such oscillations will eventually decay suggesting that weak thermalization was about time scales and not the size of the fluctuations. Nevertheless, the analyses of the size of the fluctuations were more qualitative. Here, using exact diagonalization we analyze how the size of the typical fluctuation, after long enough time for equilibration to happen, scales with the system size. For that, we use rigorous mathematical upper bounds on the equilibration of isolated quantum systems. We show that weak thermalization can be understood to be due to the small effective dimension of the initial state. Furthermore, we show that the fluctuations decay exponentially with the system size for both weak and strong thermalization indicating no sharp transitions between these two regimes.
References in corpus (15)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum mechanical evolution towards thermal equilibrium
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Strong and weak thermalization of infinite non-integrable quantum systems
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Equilibration of isolated macroscopic quantum systems
- Generalization of von Neumann's Approach to Thermalization
- Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
- Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems
- Non-ergodic extended states in the SYK model
- Equilibration time scales in closed many-body quantum systems
- Gaussian Equilibration