Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

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


David Campbell

Department of Physics,
University of Illinos,
Urbana, USA

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


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.


A Brief Introduction

MIDIT-seminars 439-440

Thursday February 25, 1999, 15.15-17.15 h

at MIDIT, Building 321, room 033, DTU

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.