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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.03007 |
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| _version_ | 1866917535156273152 |
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| author | Bianchi, Massimo Firrotta, Maurizio Sonnenschein, Jacob Weissman, Dorin |
| author_facet | Bianchi, Massimo Firrotta, Maurizio Sonnenschein, Jacob Weissman, Dorin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-dimensional chaos I: Classical and quantum mechanics Bianchi, Massimo Firrotta, Maurizio Sonnenschein, Jacob Weissman, Dorin High Energy Physics - Theory Chaotic Dynamics 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. |
| title | Multi-dimensional chaos I: Classical and quantum mechanics |
| topic | High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2510.03007 |