Ergodicity and Mixing in Quantum Dynamics

Abstract

After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixing, there may exist a third class of quantum dynamics which is characterized by a maximized entropy.

10 pages, 6 figures and 1 table

References in corpus (4)

• Foundation of Statistical Mechanics under experimentally realistic conditions
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Entropy for Quantum Pure States and Its Dynamical Relaxation

Cited by in corpus (13)

• Quantum coarse-grained entropy and thermalization in closed systems
• Dynamical quantum ergodicity from energy level statistics
• Ergodicity in randomly perturbed quantum systems
• Thermalization of noninteracting quantum systems coupled to blackbody radiation: A Lindblad-based analysis
• Generalized Wigner-von Neumann entropy and its typicality
• Genuine Quantum Chaos and Physical Distance Between Quantum States
• Microscope for Quantum Dynamics with Planck Cell Resolution
• Ergodic theory of diagonal orthogonal covariant quantum channels
• Uncovering Quantum Many-body Scars with Quantum Machine Learning
• Self-Similarity Among Energy Eigenstates
• Probabilistic Hysteresis from a Quantum Phase Space Perspective
• Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems
• Definitions and Evolutions of Statistical Entropy for Hamiltonian Systems