Stochastic resonance in the Fermi-Pasta-Ulam chain.

A Symmetric Normal Form for the Fermi Pasta Ulam Chain

The Fermi Pasta Ulam chain with periodic boundary conditions admits discrete and continuous symmetries. These symmetries allow one to formulate important restrictions on the Birkhoff normal form of this Hamiltonian system. We derive integrability properties and KAM statements. Hence the combination of symmetry and resonance in the periodic Fermi Pasta Ulam chain explains its quasiperiodic behav...

Solitary waves in a nonintegrable Fermi-Pasta-Ulam chain.

We present a family of exact solutions describing discrete solitary waves in a nonintegrable Fermi-Pasta-Ulam chain. The family is sufficiently rich to cover the whole spectrum of known behaviors from delocalized quasicontinuum waves moving with near-sonic velocities to highly localized anticontinuum excitations with only one particle moving at a time.

From Fermi-pasta-ulam Problem to Galaxies: the Quest for Relaxation

The major problem posed by the Fermi-Pasta-Ulam work was the relaxation (thermalization) of a many-body system. We review two approaches to this problem, the ergodic theory and Langevin (stochastic) equation ones, which have been applied for the description of statistical mechanics of stellar systems. Among the particular problems that we consider, are 1-dimensional long-range interacting syste...

Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains.

The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in thermal equilibrium are studied from both statistical and wave resonance perspectives. It is shown that, even in a strongly nonlinear regime, the chain in thermal equilibrium can be effectively described by a system of weakly interacting renormalized nonlinear waves that possess (i) the Rayleigh-Jeans distribution...

Parallelization of the Numerical Lyapunov Calculation for the Fermi-Pasta-Ulam Chain