Enrico Fermi’s excursions through the fields of classical physics: Watching the landscapes of phase space and the nature of dynamical paths, looking for ergodicity
Year: 2002
Authors: Cipriani P.
Autors Affiliation: Istituto Nazionale di Ottica Applicata, largo E. Fermi 6, 50125 Firenze, Italy;
ICRA, I-65122 Pescara, Italy
CSS, I-02047 Poggio Mirteto, RI Italy
Abstract: The (relatively few) works of Fermi within the fields of classical physics had, and still have, a deep impact on our Understanding of the structure of phase space of generic nonlinear systems, along with the relative implications on the justification of a statistical description of macroscopic systems and the approach towards equilibrium. One of those milestones along the path to reconcile microscopic dynamics with macroscopic description is the first inverse experiment, performed by Fermi, Pasta, Ulam and Tsingou on an one-dimensional anharmonic chain (FPU model). After a brief historical introduction whose aim is mainly to show how that revolutionary experiment frames perfectly into Fermi’s personality, I discuss how this model, and particularly the philosophy beyond it, can be considered, still today, a valid conceptual paradigm. I show how to obtain analytical estimates of dynamic and geometric quantities through which it is possible to generalize the existing definitions of chaoticity indicators and of the threshold marking the onset of strong chaos. Nevertheless, as far as some of the most recent successful approaches to FPU problem are concerned, I outline how these cannot be generalized painlessly. Discussing in some details why they work for FPU-like models, we meet with the difficulties and troubles emerging when trying to applying them to peculiar Hamiltonian systems, for which these methodologies can give, at most, just some hints on their macroscopic behaviour. In particular. I review some conceptual and technical aspects of the combined use of the geometrical transcription of dynamics and the theory of stochastic differential equations, pointing out the issues preventing a direct extension to more general systems. Notwithstanding, this analysis gives noteworthy hints even on the much more controversial issue of a statistical description of gravitationally interacting N-body systems, furthermore allowing to understand some seemingly inconsistent results existing in the literature.
Journal/Review: IL NUOVO CIMENTO B
Volume: 117 (9-11) Pages from: 1043 to: 1066
KeyWords: nonlinear hamiltonian systems; n-body systems; Connecting to view paper tab on IsiWeb: Click here