CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS

UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR

KREKOVA 2 SI-2000 MARIBOR SLOVENIA

Phone +(386) (2) 2355 350 and 2355 351 Fax +(386) (2) 2355 360

Robnik@uni-mb.si www.camtp.uni-mb.si

PROF.DR. MARKO ROBNIK, DIRECTOR

**Abstract:**
I shall report on some recent numerical studies of statistical distributions of orbits in weakly chaotic regimes of multi-dimensional Hamiltonian system. I will show that, when chaos is limited to small phase space regimes, long – lived quasi-stationary states (QSS) exist whose statistics is well approximated for long times not by Gaussians (as one might expect from Boltzmann – Gibbs statistical mechanics) but by q - Gaussian functions of Tsallis’ Nonextensive Thermodynamics, which has been shown to apply successfully to physical systems with long range interactions. These QSS often exhibit a transition to true Gaussians (q=1), thus allowing us to identify regimes of weak diffusion and predict the occurrence of important physical phenomena such as energy equipartition in FPU chains and dynamical phase transitions in microplasma systems. Most of the material presented in these lectures is contained in a book by T. Bountis and H. Skokos, "Complex Hamiltonian Dynamics", Springer, which is expected to appear in print in 2011.

**Seminarsko predavanje bo v četrtek 27. oktobra ob 15:15 uri
v seminarski sobi CAMTP, Krekova 2, pritličje desno.
Vljudno vabljeni vsi zainteresirani, tudi
študentje.**

Prof.Dr. Marko Robnik

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