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Multi-dimensional chaos I: Classical and quantum mechanics
by Massimo Bianchi, Maurizio Firrotta, Jacob Sonnenschein, Dorin Weissman
Submission summary
| Authors (as registered SciPost users): | Dorin Weissman |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2510.03007v2 (pdf) |
| Code repository: | https://github.com/dorinw/string-chaos/ |
| Date submitted: | Dec. 5, 2025, 10:25 a.m. |
| Submitted by: | Dorin Weissman |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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 spacings between the extrema of this function. We show that these follow a repulsive Gaussian beta-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 case 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
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motivated.
It provides a novel and synergetic link between different research
areas (string theory and chaos).
Since the results rely heavily on numerical analysis, it is important
to assess their robustness.
To avoid repeating similar questions for
multiple sections, I focus on the results presented in Section 3.2 as
a representative example.
What does “very near λ=1” mean quantitatively? How do the results
change if this cutoff is modified?
The authors state that certain choices are made “because of
computational constraints.” Could these constraints be specified more
explicitly? How do they affect the results, and what is the expected
magnitude of numerical errors?
In Figure 8, ε=0.2, while the values of ks differ by 0.5, which
appears relatively large compared to the scale set by ε.
What happens if this difference is reduced to 0.1, 0.05, or 0.01?
Additionally, how do the results behave for different values of ε that are not extremely small?
Another example is "well fitted" in section "II Distribution of nearest neighbor spacings". Which is the chi square? Also how good is the "Best fit" of Table 1?
Minor comments:
The authors use "erratic" and "chaotic". Are they really the same thing ?
A sign is missing in the first (unnumbered) equation in Subsection 2.1.
The color map in Figure 4 does not indicate a minimum value.
Recommendation
Ask for minor revision