Lattice Wind-Tree Models. II. Analytic Property
- 1 September 1972
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 13 (9) , 1315-1317
- https://doi.org/10.1063/1.1666138
Abstract
Three lattice versions of the wind-tree model of Ehrenfest are studied. It is shown that various moments, including the recurrence time and the Cesaro limits limT→∞ (1/T)∑t=1TΔ(t) of the mean-square displacement Δ(t) and of the one-particle distribution ρ(t, x) at time t, are analytic functions of the reciprocal of the fugacity of the trees, or equivalently of the deviation 1-ρ of the density ρ of the trees from their close packing density 1, in certain disks in the complex plane. Two of the models were considered in Paper I, but the third is new.Keywords
This publication has 1 reference indexed in Scilit:
- Lattice Wind-Tree Models. I. Absence of DiffusionJournal of Mathematical Physics, 1972