Statistical analysis of level spacing ratios in pseudo-integrable systems: semi-Poisson insight and beyond
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915298190295040 |
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| author | Akhshani, Afshin Białous, Małgorzata Sirko, Leszek |
| author_facet | Akhshani, Afshin Białous, Małgorzata Sirko, Leszek |
| contents | We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like (zero-range) perturbation was experimentally simulated by a flat rectangular resonator with wire antennas. We show that the system exhibits semi-Poisson behavior in the frequency range $8 <ν< 16 $ GHz. The probability distribution $P(r)$ of the studied system is characterized by the parameter $ξ=0.97 \pm 0.03 $, with the expected value $ξ=1$ for the short-range plasma model. Furthermore, we provide a theoretical expression for the higher-order non-overlapping probability distribution $P_{\mathrm{sP}}^k(r)$, $k \geq 1$, in the semi-Poisson regime, incorporating long-range spectral correlations between levels. The experimental and numerical results confirm the pseudo-integrability of the studied system. The semi-Poisson ensemble, for $k=2$, approaches the GUE distribution. In addition, the uncorrelated Poisson statistics mimic the RMT ensembles at certain $k$ values, $k=4$ for GUE and $k=7$ for GSE. This unexpected scale-dependent convergence shows how spectral statistics can exhibit chaos-like features even in non-chaotic systems, suggesting that scale-dependent analysis bridges integrable and chaotic regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical analysis of level spacing ratios in pseudo-integrable systems: semi-Poisson insight and beyond Akhshani, Afshin Białous, Małgorzata Sirko, Leszek Quantum Physics We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like (zero-range) perturbation was experimentally simulated by a flat rectangular resonator with wire antennas. We show that the system exhibits semi-Poisson behavior in the frequency range $8 <ν< 16 $ GHz. The probability distribution $P(r)$ of the studied system is characterized by the parameter $ξ=0.97 \pm 0.03 $, with the expected value $ξ=1$ for the short-range plasma model. Furthermore, we provide a theoretical expression for the higher-order non-overlapping probability distribution $P_{\mathrm{sP}}^k(r)$, $k \geq 1$, in the semi-Poisson regime, incorporating long-range spectral correlations between levels. The experimental and numerical results confirm the pseudo-integrability of the studied system. The semi-Poisson ensemble, for $k=2$, approaches the GUE distribution. In addition, the uncorrelated Poisson statistics mimic the RMT ensembles at certain $k$ values, $k=4$ for GUE and $k=7$ for GSE. This unexpected scale-dependent convergence shows how spectral statistics can exhibit chaos-like features even in non-chaotic systems, suggesting that scale-dependent analysis bridges integrable and chaotic regimes. |
| title | Statistical analysis of level spacing ratios in pseudo-integrable systems: semi-Poisson insight and beyond |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.16656 |