title: Poisson-to-Wigner crossover transition in the nearest-neighbor statistics of random points on fractals.
abstract: We show that the nearest-neighbor spacing distribution for a model that consists of random points uniformly distributed on a self-similar fractal is the Brody distribution of random matrix theory. In the usual context of Hamiltonian systems, the Brody parameter does not have a definite physical meaning, but in the model considered here, the Brody parameter is actually the fractal dimension. Exploiting this result, we introduce a new model for a crossover transition between Poisson and Wigner statistics: random points on a continuous family of self-similar curves with fractal dimensions between 1 and 2. The implications to quantum chaos are discussed, and a connection to conservative classical chaos is introduced.
authors.affiliation: Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1.
authors.forename: Jamal
authors.initials: J
authors.lastname: Sakhr
authors.forename: John M
authors.initials: JM
authors.lastname: Nieminen