The Legacy of FPU

David Campbell, Provost, Boston University,

The study of the Fermi-Pasta-Ulam (FPU) “problem,” which began in Los Alamos in the early 1950s and produced results characterized by Fermi as “a suprising little discovery,” was a in fact a defining event in computational and nonlinear physics. It marked the first systematic study of a nonlinear system by digital computers (“experimental mathematics”), the birth of “nonlinear science,” and led directly to the development of the concept of “solitons” and indirectly to the modern understanding of “deterministic chaos.” In this talk, I will survey the legacy of this pioneering work, examine some present on-going studies, and predict the future implications of this watershed problem.

Beginning with a discussion of the nature of the FPU problem and the results of the original simulations, including the remarkable “FPU recurrences,” I show how a continuum limit analysis clarifies the nature of these recurrences and leads directly to the equations to which the concept of solitons was first applied. I next establish the existence of deterministic chaos in the FPU problem and discuss briefly recent attempts to clarify the transition between the solitonic and chaotic regimes. I will show how investigations derived from the FPU problem have clarified several outstanding problems in physics, including anomalous heat transport in real low-dimensional materials, the existence of “intrinsic localized modes, and the origins of statistical mechanics.