Statistical Features of High-Dimensional Hamiltonian Systems
Statistical Mechanics
2021-06-15 v1
Abstract
In this short review we propose a critical assessment of the role of chaos for the thermalization of Hamiltonian systems with high dimensionality. We discuss this problem for both classical and quantum systems. A comparison is made between the two situations: some examples from recent and past literature are presented which support the point of view that chaos is not necessary for thermalization. Finally, we suggest that a close analogy holds between the role played by Kinchin's theorem for high-dimensional classical systems and the role played by Von Neumann's theorem for many-body quantum systems.
Cite
@article{arxiv.2106.06609,
title = {Statistical Features of High-Dimensional Hamiltonian Systems},
author = {Marco Baldovin and Giacomo Gradenigo and Angelo Vulpiani},
journal= {arXiv preprint arXiv:2106.06609},
year = {2021}
}
Comments
11 pages, 3 figures, to appear as a contribution in "EPS Grand Challenges: Physics for Society at the Horizon 2050"