MIDIT OFD CATS Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and Technical University of Denmark Building 128 Department of Chemistry Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark
Department of Physics,
University of Illinos,
3 LECTURES ON THE FERMI-PASTA-ULAM PROBLEM:
The First Half-Century
(part of DTU-course 04225)
I. Friday February 19, 1999, 10.35-10.55 h
II. Tuesday February 23, 1999, 11.30-12.50 h and 13.00-13.50 h
III. Friday February 26, 1999, 09.35-10.55 h
at MIDIT, Building 305, room 027, DTU
NOTE CORRECTED TIME SCHEDULE!
Abstract: The Fermi-Pasta-Ulam (FPU) problem, which Fermi characterized
as "a suprisingly little discovery," was a in fact a defining
event in nonlinear science. It marked the first systematic
study of a nonlinear system by digital computers and led directly
to the development of the concept of "solitons" and to a more
detailed understanding of Hamiltonian chaos. In this series of
three lectures, we review of past, examine the present, and
predict the future of this watershed nonlinear problem.
In lecture I, we discuss the nature of the model and of the original and follow-on simulations, introducing and describing the remarkable "FPU recurrences."
In lecture II, we show how a continuum limit analysis clarifies the nature of these recurrences and how it leads directly to the equations to which the concept of "solitons" was first applied.
In lecture III, we explore the consequences of FPU behavior for the transport properties of real low-dimensional materials and for the geometric interpretation of the phase space of high-dimensional Hamiltonian systems.
Abstract: From the first brief hint of its in the two-page article by
Landau in 1933, the polaron has attracted continuous attention
from both theoretical and experimental solid state physicists.
In this two-seminar series, we:
(i) discuss the basic concepts involved in the creation of polarons;
(ii) distinguish large and small polarons and bipolarons;
(iii) discuss the simplest model equation exhibiting polaronic behavior (the Nonlinear Schroedinger Equation);
(iv) explore the differences between the one-particle model of polarons and the "two-band" polaron; and
(v) mention several experimental implications of polarons and bipolarons, including optical absorptions in conducting polymers and possible models for superconductivity.