Trapping, reflection, and fragmentation in a classical model of atom-lattice collisions

Scaling and universality in Brownian motion on a stochastic harmonic oscillator chain

Diffusion of a Brownian particle along a stochastic harmonic oscillator chain is investigated. In contrast to the usually discussed Brownian motion driven by Gaussian white noise, the particle at high temperatures performs long Lévy flights. At high temperatures T the diffusion coefficient scales as D∼T^{2+α}, where the parameter α determine the average damping force ∝1/(T^{α}P) on the particle at large momentum P and at high temperature. The exponent α depends on the particle-chain interaction and chain properties. It is shown that the mean time t[over ¯]_{f} necessary to perform a flight of l lattice constant scales with l as t[over ¯]_{f}∝l^{2/3} at high temperatures and flight lengths. Last, the flight length probability distribution is found to decay as 1/l^{β} with the exponent β=4/3 being universal, i.e., independent of the model parameters.

Passage of a monomer through a nonrigid periodical substrate formed by noninteracting particles

The paper examines a classical system in one degree of freedom: a particle (monomer) interacting with a periodic lattice of independent, separated oscillators. The monomer can interact with oscillators via a short-range attractive potential force. The periodic lattice of oscillators may absorb the energy of the monomer launched at some initial velocity, but it does so in a very peculiar manner. The monomer velocity gradually decreases, approaching near some nonzero limit value. The limiting monomer velocities can assume discrete values only. This behavior of the monomer is accounted for by the existing resistance force that completely vanishes at certain monomer velocities.