Out-of-time-order correlators in quantum mechanics
Abstract The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP10(2017)138 |
| _version_ | 1811254314598924288 |
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| author | Koji Hashimoto Keiju Murata Ryosuke Yoshii |
| author_facet | Koji Hashimoto Keiju Murata Ryosuke Yoshii |
| author_sort | Koji Hashimoto |
| collection | DOAJ |
| description | Abstract The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time, which could be the reason of the difficulty for the numerical analyses to exhibit the exponential growth. |
| first_indexed | 2024-04-12T17:05:30Z |
| format | Article |
| id | doaj.art-9ddfb16694d44a47b8b0011c40f62fb4 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-12T17:05:30Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9ddfb16694d44a47b8b0011c40f62fb42022-12-22T03:23:57ZengSpringerOpenJournal of High Energy Physics1029-84792017-10-0120171013110.1007/JHEP10(2017)138Out-of-time-order correlators in quantum mechanicsKoji Hashimoto0Keiju Murata1Ryosuke Yoshii2Department of Physics, Osaka UniversityKeio UniversityKeio UniversityAbstract The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time, which could be the reason of the difficulty for the numerical analyses to exhibit the exponential growth.http://link.springer.com/article/10.1007/JHEP10(2017)138AdS-CFT CorrespondenceBlack HolesModels of Quantum Gravity |
| spellingShingle | Koji Hashimoto Keiju Murata Ryosuke Yoshii Out-of-time-order correlators in quantum mechanics Journal of High Energy Physics AdS-CFT Correspondence Black Holes Models of Quantum Gravity |
| title | Out-of-time-order correlators in quantum mechanics |
| title_full | Out-of-time-order correlators in quantum mechanics |
| title_fullStr | Out-of-time-order correlators in quantum mechanics |
| title_full_unstemmed | Out-of-time-order correlators in quantum mechanics |
| title_short | Out-of-time-order correlators in quantum mechanics |
| title_sort | out of time order correlators in quantum mechanics |
| topic | AdS-CFT Correspondence Black Holes Models of Quantum Gravity |
| url | http://link.springer.com/article/10.1007/JHEP10(2017)138 |
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