The FPU Research Program: Echoes on a String

Abstract

Even though the FPU results were not published until the two volumes of Fermi’s Collected Works came out 11 years after the fact (Segré, 1965), word of the simulation did spread to the physics community by way of private communication. At that time, physics research preceded along the two accepted lines: theory and experiment. Computer simulation was a new kind of research direction that did not yet have a plot of its own in the field of scientific research. Being a set of numerical calculations, the FPU problem seemed to fall into the category of theory. But a theoretical, pencil-and-napkin physicist was not likely to be exploring the realm of “experimental mathematics,” such as that opened-up by FPU. Although no physical experiment had been performed, the problem did have many of the effects usually associated with an experiment: theorists were faced with the implicit demand to retrodict the anomalous results of FPU, just as any scientist is challenged to explain the unexpected result of a valid physical experiment. Furthermore, the FPU model was chosen exactly because it was thought to be unsolvable using analytical means. Theory in dynamics had been stalled for nearly 50 years, but here was a new and surprising result that gave theorists renewed motivation. Further theoretical work must come from that most difficult arena known as perturbation theory.

And certainly the atoms did not move by volition, nor did they place themselves by sharp intelligence, nor did they agree what movements to produce, but they, being many and moving about in many ways, are constantly being buffeted and given motion, and by trying every kind of combination and motion, finally they fall into the arrangements and the patterns of which the sum of things consists.

Lucretius (Book I, lines 1021–1028)

The results of the computer calculations of [FPU] thus appear to be in sharp contmst, if not in actual contmdiction, to the widely held notions concerning the approach to equilibrium. . . . Consequently, aside from any element of contradiction, a number of physicists have been puzzled by the failure of [the FPU Hamiltonian] to lead to equilibrium behavior.

Joseph Ford (1961, p. 387)