Abstract
We consider a ray of light propagating within a system of infinitely many adjoining rectangles in a plane with passages between any pair of neighboring ones. The ray is assumed to be reflected by the sides of the rectangles, and is refracted while passing from one rectangle to its neighbor. We prove that if the sizes of the rectangles or the coefficients of refraction inside them are random, then with probability 1 the ray reaches arbitrarily remote rectangles.
Similar content being viewed by others
References
I. P. Kornfeld, Ya. G. Sinai, and S. V. Fomin,Ergodic Theory (Springer-Verlag, 1982).
M. Keane, Interval exchange transformation,Math. Z. 141:25–31 (1975).
H. Masur, Interval exchange transformation and measurable foliations,Ann. Math. 115:169–200 (1982).
W. Veech, Gauss measures for transformations of the space of interval exchange transformations,Ann. Math. 115:201–242 (1982).
D. J. Gates, Lattice wind-tree models. I. Absence of diffusion,J. Math. Phys. 13(7):1005–1013 (1972).
A. N. Zemlyakov and A. B. Katok, Topological transitivity of billiards in polygons,Math. Notes 18(2):760–764 (1976).
E. Gutkin, Billiards on almost integrable polyhedral surfaces,Ergodic Theory Dynamical Syst. 4:569–584 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Figotin, A. Model of a nonhomogeneous medium conducting light. J Stat Phys 69, 969–993 (1992). https://doi.org/10.1007/BF01058758
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01058758