Power spectra and autocovariances of level spacings beyond the Dyson conjecture
| Autor: | Roman Riser, Peng Tian, Eugene Kanzieper |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Quantum Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems FOS: Physical sciences Mathematical Physics (math-ph) Disordered Systems and Neural Networks (cond-mat.dis-nn) Chaotic Dynamics (nlin.CD) Exactly Solvable and Integrable Systems (nlin.SI) Condensed Matter - Disordered Systems and Neural Networks Quantum Physics (quant-ph) Nonlinear Sciences - Chaotic Dynamics Mathematical Physics |
| Zdroj: | Physical Review E. 107 |
| ISSN: | 2470-0053 2470-0045 |
| DOI: | 10.1103/physreve.107.l032201 |
| Popis: | Introduced in the early days of random matrix theory, the autocovariances $\delta I^j_k={\rm cov}(s_j, s_{j+k})$ of level spacings $\{s_j\}$ accommodate a detailed information on correlations between individual eigenlevels. It was first conjectured by Dyson that the autocovariances of distant eigenlevels in the unfolded spectra of infinite-dimensional random matrices should exhibit a power-law decay $\delta I^j_k\approx -1/\beta\pi^2k^2$, where $\beta$ is the symmetry index. In this Letter, we establish an exact link between the autocovariances of level spacings and their power spectrum, and show that, for $\beta=2$, the latter admits a representation in terms of a fifth Painlev\'e transcendent. This result is further exploited to determine an asymptotic expansion for autocovariances that reproduces the Dyson formula as well as provides the subleading corrections to it. High-precision numerical simulations lend independent support to our results. Comment: 6 pages; 1 figure; published version |
| Databáze: | OpenAIRE |
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