Level Compressibility of Certain Random Unitary Matrices
The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices describing models with intermediate spectral statistics. The computa...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/24/6/795 |
| _version_ | 1797487738212057088 |
|---|---|
| author | Eugene Bogomolny |
| author_facet | Eugene Bogomolny |
| author_sort | Eugene Bogomolny |
| collection | DOAJ |
| description | The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices describing models with intermediate spectral statistics. The computations are based on the approach developed by G. Tanner for chaotic systems. The main ingredient of the method is the determination of eigenvalues of a transition matrix whose matrix elements equal the squared moduli of matrix elements of the initial unitary matrix. The principal result of the paper is the proof that the level compressibility of random unitary matrices derived from the exact quantisation of barrier billiards and consequently of barrier billiards themselves is equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> irrespective of the height and the position of the barrier. |
| first_indexed | 2024-03-09T23:52:03Z |
| format | Article |
| id | doaj.art-dfe8d8a70f67472db79c93afd34a693e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T23:52:03Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-dfe8d8a70f67472db79c93afd34a693e2023-11-23T16:33:16ZengMDPI AGEntropy1099-43002022-06-0124679510.3390/e24060795Level Compressibility of Certain Random Unitary MatricesEugene Bogomolny0Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, FranceThe value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices describing models with intermediate spectral statistics. The computations are based on the approach developed by G. Tanner for chaotic systems. The main ingredient of the method is the determination of eigenvalues of a transition matrix whose matrix elements equal the squared moduli of matrix elements of the initial unitary matrix. The principal result of the paper is the proof that the level compressibility of random unitary matrices derived from the exact quantisation of barrier billiards and consequently of barrier billiards themselves is equal to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> irrespective of the height and the position of the barrier.https://www.mdpi.com/1099-4300/24/6/795level compressibilitybarrier billiards |
| spellingShingle | Eugene Bogomolny Level Compressibility of Certain Random Unitary Matrices Entropy level compressibility barrier billiards |
| title | Level Compressibility of Certain Random Unitary Matrices |
| title_full | Level Compressibility of Certain Random Unitary Matrices |
| title_fullStr | Level Compressibility of Certain Random Unitary Matrices |
| title_full_unstemmed | Level Compressibility of Certain Random Unitary Matrices |
| title_short | Level Compressibility of Certain Random Unitary Matrices |
| title_sort | level compressibility of certain random unitary matrices |
| topic | level compressibility barrier billiards |
| url | https://www.mdpi.com/1099-4300/24/6/795 |
| work_keys_str_mv | AT eugenebogomolny levelcompressibilityofcertainrandomunitarymatrices |