Exact time evolution of a classical harmonic-oscillator chain

Solitary waves in the granular chain

“…It is well known that in an infinite system of harmonic oscillators, the average kinetic energy per particle is constant [88] and hence the equipartition theorem is respected. The dynamics of a chain of 2D granular disks, where n = 2, in a system without boundaries has recently been exactly solved [89].…”

Dynamic Structure Factor for a Harmonic Oscillator and the Harmonic Oscillator Chain

“…An introduction of normal modes leads to a decoupling of the oscillators and thus to an effective single-particle problem, see also Ref. [9]. A detailed description of this relation is work in progress.…”

The propagation and backscattering of soliton-like pulses in a chain of quartz beads and related problems. (I). Propagation

“…The acceleration autocorrelation finction, defined below as C(t), for a tagged particle can be used to measure the relaxation of that tagged particle [21][22][23][24] as it is perturbed by an impulse and as it tries to return to its unperturbed lower energy state. It serves as a measure of the memory of the interaction .wdTeredby the tagged particle.…”