Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator
Abstract Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is classically integrable and has a Poisson-like energy...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2021)030 |
| _version_ | 1818645291574755328 |
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| author | Paul Romatschke |
| author_facet | Paul Romatschke |
| author_sort | Paul Romatschke |
| collection | DOAJ |
| description | Abstract Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is classically integrable and has a Poisson-like energy-level distribution. For low temperature, OTOCs are periodic in time, similar to results for the harmonic oscillator and the particle in a box. For high temperature, OTOCs exhibit a rapid (but power-like) rise at early times, followed by saturation consistent with 2〈x 2〉 T 〈p 2〉 T at late times. At high temperature, the spectral form factor decreases at early times, bounces back and then reaches a plateau with strong fluctuations. |
| first_indexed | 2024-12-17T00:28:25Z |
| format | Article |
| id | doaj.art-99604c4ccea743d2966ba3bb92995ce8 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T00:28:25Z |
| publishDate | 2021-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-99604c4ccea743d2966ba3bb92995ce82022-12-21T22:10:24ZengSpringerOpenJournal of High Energy Physics1029-84792021-01-012021111810.1007/JHEP01(2021)030Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillatorPaul Romatschke0Department of Physics, University of ColoradoAbstract Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is classically integrable and has a Poisson-like energy-level distribution. For low temperature, OTOCs are periodic in time, similar to results for the harmonic oscillator and the particle in a box. For high temperature, OTOCs exhibit a rapid (but power-like) rise at early times, followed by saturation consistent with 2〈x 2〉 T 〈p 2〉 T at late times. At high temperature, the spectral form factor decreases at early times, bounces back and then reaches a plateau with strong fluctuations.https://doi.org/10.1007/JHEP01(2021)030AdS-CFT CorrespondenceBlack HolesModels of Quantum Gravity |
| spellingShingle | Paul Romatschke Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator Journal of High Energy Physics AdS-CFT Correspondence Black Holes Models of Quantum Gravity |
| title | Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator |
| title_full | Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator |
| title_fullStr | Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator |
| title_full_unstemmed | Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator |
| title_short | Quantum mechanical out-of-time-ordered-correlators for the anharmonic (quartic) oscillator |
| title_sort | quantum mechanical out of time ordered correlators for the anharmonic quartic oscillator |
| topic | AdS-CFT Correspondence Black Holes Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP01(2021)030 |
| work_keys_str_mv | AT paulromatschke quantummechanicaloutoftimeorderedcorrelatorsfortheanharmonicquarticoscillator |