2000/11/30 by Prot Pakonski, Prot Pakónski, Karol Życzkowski +3
Mathematics · Physics and Astronomy · #Chaotic #Circular ensemble #Computer science #Discrete mathematics #Graph #Markov chain #Mathematical analysis #Mathematics #Physics #Piecewise #Pure mathematics #Quantum #Quantum chaos and dynamical systems #Quantum graph #Quantum mechanics #Stochastic processes and statistical mechanics #Symbolic dynamics #Theoretical and Computational Physics #Unitary matrix #Unitary state #nlin.CD #quant-ph
paper · pdf · doi:10.1088/0305-4470/34/43/313
published as J. Phys. A: Math. Gen. 34 (2001) 9303-9317 · REVTeX 13 pages, 12 figures included, final published version
openalex publication_date 2001/10/19 · arxiv created 2001/10/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a certain class of classical one-dimensional piecewise linear maps. For these systems we introduce an infinite family of Markov partitions in equal cells. The symbolic dynamics generated by these systems is described by bi-stochastic (doubly stochastic) matrices. We analyse the structure of graphs generated from the corresponding symbolic dynamics. We demonstrate that the spectra of quantized graphs corresponding to the regular classical systems have locally Poissonian statistics, while quantized graphs derived from classically chaotic systems display statistical properties characteristic of the circular unitary ensemble, even though the corresponding unitary matrices are sparse.