Statistics and complexity of wavefunction spreading in quantum dynamical systems
Abstract We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability distribution of the results of measurements of this spreadi...
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| Format: | Article |
| Language: | English |
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2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)139 |
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| author | Yichao Fu Keun-Young Kim Kunal Pal Kuntal Pal |
| author_facet | Yichao Fu Keun-Young Kim Kunal Pal Kuntal Pal |
| author_sort | Yichao Fu |
| collection | DOAJ |
| description | Abstract We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability distribution of the results of measurements of this spreading operator at a certain instant of time, and compute the characteristic function of this distribution. We show that the moments of this characteristic function are related to the so-called generalised spread complexities, and obtain expressions for them in several cases when the Hamiltonian is an element of a Lie algebra. Furthermore, by considering a continuum limit of the Krylov basis, we show that the generalised spread complexities of higher orders have a peak in the time evolution for a random matrix Hamiltonian belonging to the Gaussian unitary ensemble. We also obtain an upper bound in the change in generalised spread complexity at an arbitrary time in terms of the operator norm of the Hamiltonian and discuss the significance of these results. |
| format | Article |
| id | doaj-art-dcb49f4498da47dfad5f938546e4aec0 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-dcb49f4498da47dfad5f938546e4aec02025-08-20T03:45:39ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025613510.1007/JHEP06(2025)139Statistics and complexity of wavefunction spreading in quantum dynamical systemsYichao Fu0Keun-Young Kim1Kunal Pal2Kuntal Pal3Department of Physics and Photon Science, Gwangju Institute of Science and TechnologyDepartment of Physics and Photon Science, Gwangju Institute of Science and TechnologyAsia Pacific Center for Theoretical PhysicsDepartment of Physics and Photon Science, Gwangju Institute of Science and TechnologyAbstract We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability distribution of the results of measurements of this spreading operator at a certain instant of time, and compute the characteristic function of this distribution. We show that the moments of this characteristic function are related to the so-called generalised spread complexities, and obtain expressions for them in several cases when the Hamiltonian is an element of a Lie algebra. Furthermore, by considering a continuum limit of the Krylov basis, we show that the generalised spread complexities of higher orders have a peak in the time evolution for a random matrix Hamiltonian belonging to the Gaussian unitary ensemble. We also obtain an upper bound in the change in generalised spread complexity at an arbitrary time in terms of the operator norm of the Hamiltonian and discuss the significance of these results.https://doi.org/10.1007/JHEP06(2025)139Gauge-Gravity CorrespondenceHolography and Condensed Matter Physics (AdS/CMT) |
| spellingShingle | Yichao Fu Keun-Young Kim Kunal Pal Kuntal Pal Statistics and complexity of wavefunction spreading in quantum dynamical systems Journal of High Energy Physics Gauge-Gravity Correspondence Holography and Condensed Matter Physics (AdS/CMT) |
| title | Statistics and complexity of wavefunction spreading in quantum dynamical systems |
| title_full | Statistics and complexity of wavefunction spreading in quantum dynamical systems |
| title_fullStr | Statistics and complexity of wavefunction spreading in quantum dynamical systems |
| title_full_unstemmed | Statistics and complexity of wavefunction spreading in quantum dynamical systems |
| title_short | Statistics and complexity of wavefunction spreading in quantum dynamical systems |
| title_sort | statistics and complexity of wavefunction spreading in quantum dynamical systems |
| topic | Gauge-Gravity Correspondence Holography and Condensed Matter Physics (AdS/CMT) |
| url | https://doi.org/10.1007/JHEP06(2025)139 |
| work_keys_str_mv | AT yichaofu statisticsandcomplexityofwavefunctionspreadinginquantumdynamicalsystems AT keunyoungkim statisticsandcomplexityofwavefunctionspreadinginquantumdynamicalsystems AT kunalpal statisticsandcomplexityofwavefunctionspreadinginquantumdynamicalsystems AT kuntalpal statisticsandcomplexityofwavefunctionspreadinginquantumdynamicalsystems |