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**Harvard**

Wennberg, B. (2012) *Free Path Lengths in Quasi Crystals*.

** BibTeX **

@article{

Wennberg2012,

author={Wennberg, Bernt},

title={Free Path Lengths in Quasi Crystals},

journal={Journal of Statistical Physics},

issn={0022-4715},

volume={147},

issue={5},

pages={981-990},

abstract={The Lorentz gas is a model for a cloud of point particles (electrons) in a distribution of scatterers in space. The scatterers are often assumed to be spherical with a fixed diameter d, and the point particles move with constant velocity between the scatterers, and are specularly reflected when hitting a scatterer. There is no interaction between point particles. An interesting question concerns the distribution of free path lengths, i.e. the distance a point particle moves between the scattering events, and how this distribution scales with scatterer diameter, scatterer density and the distribution of the scatterers. It is by now well known that in the so-called Boltzmann-Grad limit, a Poisson distribution of scatterers leads to an exponential distribution of free path lengths, whereas if the scatterer distribution is periodic, the free path length distribution asymptotically behaves as a power law. This paper considers the case when the scatters are distributed on a quasi crystal, i.e. non periodically, but with a long range order. Simulations of a one-dimensional model are presented, showing that the quasi crystal behaves very much like a periodic crystal, and in particular, the distribution of free path lengths is not exponential.},

year={2012},

keywords={Lorentz gas, Quasi crystal, Free path lengths, periodic lorentz gas, boltzmann-grad limit, equation },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 160517

A1 Wennberg, Bernt

T1 Free Path Lengths in Quasi Crystals

YR 2012

JF Journal of Statistical Physics

SN 0022-4715

VO 147

IS 5

SP 981

OP 990

AB The Lorentz gas is a model for a cloud of point particles (electrons) in a distribution of scatterers in space. The scatterers are often assumed to be spherical with a fixed diameter d, and the point particles move with constant velocity between the scatterers, and are specularly reflected when hitting a scatterer. There is no interaction between point particles. An interesting question concerns the distribution of free path lengths, i.e. the distance a point particle moves between the scattering events, and how this distribution scales with scatterer diameter, scatterer density and the distribution of the scatterers. It is by now well known that in the so-called Boltzmann-Grad limit, a Poisson distribution of scatterers leads to an exponential distribution of free path lengths, whereas if the scatterer distribution is periodic, the free path length distribution asymptotically behaves as a power law. This paper considers the case when the scatters are distributed on a quasi crystal, i.e. non periodically, but with a long range order. Simulations of a one-dimensional model are presented, showing that the quasi crystal behaves very much like a periodic crystal, and in particular, the distribution of free path lengths is not exponential.

LA eng

DO 10.1007/s10955-012-0500-3

LK http://dx.doi.org/10.1007/s10955-012-0500-3

OL 30