Propagation and organization in lattice random media

Details Propagation and organization in lattice random media Propagation and organization in lattice random media

1999-05-12

arxiv.org/abs/cond-mat/9905168v1

Physics

Condensed Matter

Statistical Mechanics

30 pages, 15 separate figures (in PostScript); submitted to J. Stat. Phys

Scientific paper

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are occupied by scatterers with the following properties: (i) the state of each site is defined by its spin (up or down); (ii) the particle arriving at a site is scattered forward (backward) if the spin is up (down); (iii) the state of the site is modified by the passage of the particle, i.e. the spin of the site where a scattering has taken place, flips ($\uparrow \Leftrightarrow \downarrow $). We consider one dimensional and triangular lattices, for which we give a microscopic description of the dynamics, prove the propagation of a particle through the scatterers, and compute analytically its statistical properties. In particular we prove that, in one dimension, the average propagation velocity is $ = 1/(3-2q)$, with $q$ the probability that a site has a spin $\uparrow$, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: $ = 1/8$. In both cases, the origin of the propagation is a blocking mechanism, restricting the motion of the particle in the direction opposite to the ultimate propagation direction, and there is a specific re-organization of the spins after the passage of the particle. A detailed mathematical analysis of this phenomenon is, to the best of our knowledge, presented here for the first time.

Affiliated with

Also associated with

No associations

Rating

Propagation and organization in lattice random media does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Propagation and organization in lattice random media, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Propagation and organization in lattice random media will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-47781