Equipartition times in a Fermi-Pasta-Ulam system

Pages: 710 - 719, Issue Special, August 2005

 Abstract        Full Text (349.0K)              

Simone Paleari - Dipartimento di Matematica “F. Enriques”, Universita di Milano, Via Saldini 50, 20133 Milano, Italy (email)
Tiziano Penati - Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R. Cozzi 53, 20125 - Milano, Italy (email)

Abstract: We investigate with numerical methods the celebrated Fermi-Pasta- Ulam model, a chain of non-linearly coupled oscillators with identical masses. We are interested in the evolution towards equipartition when energy is initially given to one or a few modes. In previous works we considered the initial energy being given on the lower part of the spectrum. Using the spectral entropy as a numerical indicator we obtained a strong indication that the relaxation time to equipartition increases exponentially with an inverse power of the specific energy. Such a scaling appears to remain valid in the thermodynamic limit. In this paper we explore the dynamics obtained with the initial excitation on the high frequency modes, and we obtain also in this case indication of exponentially long times to equipartition.

Keywords:  FPU, thermodynamic limit, equipartition.
Mathematics Subject Classification:  Primary: 34C15, 70K55; Secondary: 34C28.

Received: September 2004;      Revised: March 2005;      Published: September 2005.