English

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.

Keywords

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"

R2 v1 2026-06-24T03:07:05.505Z