Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and Revivals
The quantum evolution of wave functions controlled by the spectrum of Lévy random matrices is considered. An analytical treatment of quantum recurrences and revivals in the Hilbert space is performed in the framework of a theory of almost periodic functions. It is shown that the statistics of quantu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/171 |
| _version_ | 1827672372145029120 |
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| author | Alexander Iomin |
| author_facet | Alexander Iomin |
| author_sort | Alexander Iomin |
| collection | DOAJ |
| description | The quantum evolution of wave functions controlled by the spectrum of Lévy random matrices is considered. An analytical treatment of quantum recurrences and revivals in the Hilbert space is performed in the framework of a theory of almost periodic functions. It is shown that the statistics of quantum recurrences in the Hilbert space of quantum systems is sensitive to the statistics of the corresponding quantum spectrum. In particular, it is shown that both the Poisson energy level statistics and the Brody distribution correspond to the power law of the quantum recurrences, while the Wigner–Dyson and Lévy–Smirnov statistics of the energy spectra are responsible for the exponential statistics of the quantum returns of the wave function. |
| first_indexed | 2024-03-10T04:05:33Z |
| format | Article |
| id | doaj.art-9a60933d865e446b86c5c6dc31500eb7 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:33Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-9a60933d865e446b86c5c6dc31500eb72023-11-23T08:23:14ZengMDPI AGFractal and Fractional2504-31102021-10-015417110.3390/fractalfract5040171Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and RevivalsAlexander Iomin0Department of Physics, Technion, Haifa 32000, IsraelThe quantum evolution of wave functions controlled by the spectrum of Lévy random matrices is considered. An analytical treatment of quantum recurrences and revivals in the Hilbert space is performed in the framework of a theory of almost periodic functions. It is shown that the statistics of quantum recurrences in the Hilbert space of quantum systems is sensitive to the statistics of the corresponding quantum spectrum. In particular, it is shown that both the Poisson energy level statistics and the Brody distribution correspond to the power law of the quantum recurrences, while the Wigner–Dyson and Lévy–Smirnov statistics of the energy spectra are responsible for the exponential statistics of the quantum returns of the wave function.https://www.mdpi.com/2504-3110/5/4/171Lévy matrixHilbert spacePoincaré recurrencesstatistics of quantum spectrumalmost periodic functionsquantum revivals |
| spellingShingle | Alexander Iomin Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and Revivals Fractal and Fractional Lévy matrix Hilbert space Poincaré recurrences statistics of quantum spectrum almost periodic functions quantum revivals |
| title | Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and Revivals |
| title_full | Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and Revivals |
| title_fullStr | Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and Revivals |
| title_full_unstemmed | Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and Revivals |
| title_short | Quantum Walks in Hilbert Space of Lévy Matrices: Recurrences and Revivals |
| title_sort | quantum walks in hilbert space of levy matrices recurrences and revivals |
| topic | Lévy matrix Hilbert space Poincaré recurrences statistics of quantum spectrum almost periodic functions quantum revivals |
| url | https://www.mdpi.com/2504-3110/5/4/171 |
| work_keys_str_mv | AT alexanderiomin quantumwalksinhilbertspaceoflevymatricesrecurrencesandrevivals |