Power spectrum of the circular unitary ensemble
| Autor: | Eugene Kanzieper, Roman Riser |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Quantum Physics
Probability (math.PR) FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Nonlinear Sciences - Chaotic Dynamics Condensed Matter Physics FOS: Mathematics Chaotic Dynamics (nlin.CD) Quantum Physics (quant-ph) Mathematical Physics Mathematics - Probability |
| Zdroj: | Physica D: Nonlinear Phenomena. 444:133599 |
| ISSN: | 0167-2789 |
| DOI: | 10.1016/j.physd.2022.133599 |
| Popis: | We study the power spectrum of eigen-angles of random matrices drawn from the circular unitary ensemble ${\rm CUE}(N)$ and show that it can be evaluated in terms of either a Fredholm determinant, or a Toeplitz determinant, or a sixth Painlev\'e function. In the limit of infinite-dimensional matrices, $N\rightarrow\infty$, we derive a ${\it\, concise\,}$ parameter-free formula for the power spectrum which involves a fifth Painlev\'e transcendent and interpret it in terms of the ${\rm Sine}_2$ determinantal random point field. Further, we discuss a universality of the predicted power spectrum law and tabulate it (follow http://eugenekanzieper.faculty.hit.ac.il/data.html) for easy use by random-matrix-theory and quantum chaos practitioners. Comment: 47 pages; 4 figures; published version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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