Integrable-like behavior in the Fermi-Pasta-Ulam model

Host Institution:

La Trobe University

Title of Seminar:

Integrable-like behavior in the Fermi-Pasta-Ulam model

Speaker's Name:

Dr Heleni Christodoulidi

Speaker's Institution:

Patras University, Greece

Time and Date:

Monday 18 November, 4.00pm (AEDT)

Seminar Abstract:

In 1950’s Fermi, motivated by fundamental questions of statistical mechanics, started a numerical experiment in collaboration with Pasta and Ulam to test the ergodic properties of nonlinear dynamical systems. The chosen so-called FPU system was a one dimensional chain of N nonlinear coupled oscillators, described by a quadratic potential of nearby particle interactions plus a cubic perturbation. Fermi’s ergodic hypothesis states that a system under an arbitrarily small perturbing force becomes generically ergodic. Starting with the longest wavelength normal mode, the FPU system showed a non-ergodic behavior. Many pioneer works followed for the explanation of this paradox. The most prominent of them have been the work of Zabusky and Kruskal (1965), with evidence of connection between the FPU system in the thermodynamic limit and the pde Korteweg-de Vries, and the work of Flaschka et al. (1982), where the authors discovered a similar behavior of the FPU model in the Toda chain. Recent developments show a more complete picture of the problem and its explanation.

 

 

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