# Derivation of a linear Boltzmann equation for a lattice gas

@inproceedings{Caglioti1999DerivationOA, title={Derivation of a linear Boltzmann equation for a lattice gas}, author={Emanuele Caglioti and Mario Pulvirenti and Vincent L. Ricci}, year={1999} }

- Published 1999

We consider a Lorentz gas in the plane where the scatterers have random positions on a square lattice. The scatterers are identical disks of diameter , which is also the size of the side of a cell and the probability, for a given cell, to be occupied by a scatterer. A point particle moves freely between the scatterers, interacting with them through elastic collisions. We show that, when "! 0, the probability density of such a light particle converges to the solution of the linear Boltzmann… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-6 OF 6 CITATIONS

## Spherical averages in the space of marked lattices

VIEW 2 EXCERPTS

CITES BACKGROUND

## Free Path Lengths in Quasi Crystals

VIEW 2 EXCERPTS

CITES BACKGROUND

## Non Markovian Behavior of the Boltzmann-Grad Limit of Linear Stochastic Particle Systems

VIEW 1 EXCERPT

CITES METHODS

## THE BOLTZMANN-GRAD LIMIT OF A STOCHASTIC LORENTZ GAS IN A FORCE FIELD

VIEW 2 EXCERPTS

CITES BACKGROUND

## The weak-coupling limit of large classical and quantum systems

VIEW 1 EXCERPT

CITES METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-6 OF 6 REFERENCES

## On the distribution of free path lenghts for the periodic lorentz gas

VIEW 1 EXCERPT

## On the Boltzmann equation for the Lorentz gas

VIEW 1 EXCERPT

## Ergodic Theory

VIEW 1 EXCERPT

## The Lorentz process converges to a random flight process

VIEW 1 EXCERPT

## The theory of stochastic processes

VIEW 1 EXCERPT