Adiabatic Invariants and Time Scales for Energy Sharing in Models of Classical Gases
The purpose of this paper is twofold. On one hand I would like to illustrate an application of the theory of adiabatic invariants — essentially, Nekhoroshev-like exponential laws — to classical statistical mechanics. On the other hand, I would like to revisit some ideas of distinguished physicists, like Jeans and Landau, who long time ago, much before modern perturbation theory, introduced exponential laws in connection with problems of adiabatic invariance (Jeans,1,2 1903 and 1905; Landau and Teller,3 1936). These authors worked only heuristically, as physicists often do, but their ideas are definitely deep, and as we shall see, at least in some cases their heuristic arguments can be turned into effective proofs.
KeywordsEnergy Exchange Vibrational Energy Fourier Component Classical Statistical Mechanic Adiabatic Invariant
Unable to display preview. Download preview PDF.
- D. Ter Haar (ed.) Collected Papers of L. D. Landau, (Pergamon Press, Oxford, 1965), page 147.Google Scholar
- 10.G. Benettin, A. Carati and P. Sempio, On the Landau-Teller approximation for the energy exchanges with fast degrees of freedom, to appear in Journ. Stat. Phys. (1993).Google Scholar
- 11.G. Benettin and A. Giorgilli, On the Hamiltonian interpolation of near to the identity symplectic mappings, with application to symplectic integration algorithms, preprint 1993.Google Scholar
- 13.A. Carati, Ph.D. Thesis and paper in preparation.Google Scholar
- 14.G. Benettin, A. Carati and G. Gallavotti, paper in preparation.Google Scholar
- 15.J. Moser, Lectures on Hamiltonian Systems, in Mem. American Math. Soc. No 81, 1 (1968).Google Scholar
- 16.A.I. Neishtadt, Prikl. Matem. Mekan. 45, 80 (1982) [PMM U.S.S.R. 45, 58 (1982)].Google Scholar