2005/10/27 by Jamal Sakhr, John M. Nieminen, J. M. Nieminen · 20 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Artificial intelligence #Chaos control and synchronization #Computer science #Crossover #Eigenvalues and eigenvectors #Fractal #Fractal dimension #Mathematical analysis #Mathematics #Physics #Poisson distribution #Protein Structure and Dynamics #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Statistical physics #Statistics #nlin.CD
paper · pdf · doi:10.1103/physreve.72.045204
published in Physical Review E 72(4), 045204 (American Physical Society) · Low-resolution figure is included here. Full resolution image available (upon request) from the authors
openalex publication_date 2005/10/27 · arxiv created 2005/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.