The monoatomic FPU system as a limit of a diatomic FPU system
Abstract
We consider a diatomic infinite Fermi-Pasta-Ulam (FPU) system with light and
heavy particles. For a small mass ratio, we prove error estimates for the
approximation of the dynamics of this system by the dynamics of the monoatomic
FPU system. The light particles are squeezed by the heavy particles at the mean
value of their displacements. The error estimates are derived by means of the
energy method and hold for sufficiently long times, for which the dynamics of
the monoatomic FPU system is observed. The approximation result is restricted
to sufficiently small displacements of the heavy particles relatively to each
other.