2025/10/03 by Massimo Bianchi, Bianchi, Massimo, Maurizio Firrotta +5
Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum chaos and dynamical systems #Quantum many-body systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2510.03007
openalex publication_date 2025/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This release includes code and supplementary figures used for the paper Multi-dimensional Chaos I: Classical and quantum mechanics (arXiv:hep-th/2510.03007). Abstract: We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball system. In the former case it is illustrated by means of two-dimensional plots of the scattering angle and of the number of bounces. We draw similar patterns for the quantum differential cross-section for various geometries of the disks. We find that the eigenvalues of the S-matrix are distributed according to the Circular Orthogonal Ensemble (COE) in random matrix theory (RMT), provided the setup be asymmetric and the wave-number be large enough. We then consider the electric potential associated with charges randomly located on a plane as a toy model that generalizes the scattering from a leaky torus. We propose several methods to analyze the distribution of spacings between the extrema of such functions. We show that these follow a repulsive Gaussian β-ensemble distribution even for Poisson-distributed positions of the charges. A generalization of the spectral form factor is introduced and determined. We apply these methods to the cases of a chaotic S-matrix and of the quantum pinball scattering. The spacings between nearest neighbor extrema points and ratios between adjacent spacings follow a logistic and Beta distributions correspondingly. We conjecture about a potential relation with random tensor theory.