# Statistical Features of High-Dimensional Hamiltonian Systems

@inproceedings{Baldovin2021StatisticalFO, title={Statistical Features of High-Dimensional Hamiltonian Systems}, author={M. Baldovin and G. Gradenigo and A. Vulpiani}, year={2021} }

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… Expand

#### References

SHOWING 1-10 OF 42 REFERENCES

Statistical Mechanics of an Integrable System

- Physics
- 2020

We provide here an explicit example of the Khinchin's ideas that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics and it is… Expand

Chaotic behavior in nonlinear Hamiltonian systems and equilibrium statistical mechanics

- Physics
- 1987

The relation between chaotic dynamics of nonlinear Hamiltonian systems and equilibrium statistical mechanics in its canonical ensemble formulation has been investigated for two different nonlinear… Expand

Transition, Ergodicity and Lyapunov Spectra of Hamiltonian Dynamical Systems

- Physics
- 1987

Hamiltonian systems on a one-dimensional lattice with discrete time are studied. As the coupling constant is increased, they show a sharp transition from regular to random motion. Below the… Expand

Distribution of characteristic exponents in the thermodynamic limit

- Physics
- 1986

The existence of the thermodynamic limit for the spectrum of the Lyapunov characteristic exponents is numerically investigated for the Fermi-Pasta-Ulam p model. We show that the shape of the spectrum… Expand

On the Tendency Toward Ergodicity with Increasing Number of Degrees of Freedom in Hamiltonian Systems

- Mathematics
- 1994

Numerical experiments on a symplectic coupled map system are performed to investigate the tendency for global ergodic behavior of typical Hamiltonian systems as the number of degrees of freedom N is… Expand

Long-time behavior of macroscopic quantum systems

- Physics, Mathematics
- 2010

AbstractThe renewed interest in the foundations of quantum statistical mechanics in recent years
has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We
have found this… Expand

The Fermi-Pasta-Ulam problem : a status report

- Mathematics
- 2008

to FPU.- Dynamics of Oscillator Chains.- Role of Chaos for the Validity of Statistical Mechanics Laws: Diffusion and Conduction.- The Fermi-Pasta-Ulam Problem and the Metastability Perspective.-… Expand

Proof of the ergodic theorem and the H-theorem in quantum mechanics

- Physics
- 2010

AbstractIt is shown how to resolve the apparent contradiction between the macroscopic approach of
phase space and the validity of the uncertainty relations. The main notions of statistical
mechanics… Expand

Alternatives to eigenstate thermalization.

- Physics, Medicine
- Physical review letters
- 2012

It is shown that von Neumann's quantum ergodic theorem relies on an assumption that is essentially equivalent to ETH, and whether, following a sudden quench, special classes of pure states can lead to thermal behavior in systems that do not obey ETH, namely, integrable systems. Expand

Asymptotic Form of the Structure Function for Real Systems

- Physics
- 1963

It is shown that the asymptotic formula for the structure function obtained by Khinchin for the case of a system of n noninteracting components, also holds for a classical system of N interacting… Expand