### 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.

Original language | English |
---|---|

Article number | 138 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2017 Oct 1 |

### Fingerprint

### Keywords

- AdS-CFT Correspondence
- Black Holes
- Models of Quantum Gravity

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2017*(10), [138]. https://doi.org/10.1007/JHEP10(2017)138

**Out-of-time-order correlators in quantum mechanics.** / Hashimoto, Koji; Murata, Keiju; Yoshii, Ryosuke.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2017, no. 10, 138. https://doi.org/10.1007/JHEP10(2017)138

}

TY - JOUR

T1 - Out-of-time-order correlators in quantum mechanics

AU - Hashimoto, Koji

AU - Murata, Keiju

AU - Yoshii, Ryosuke

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Black Holes

KW - Models of Quantum Gravity

UR - http://www.scopus.com/inward/record.url?scp=85032278508&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032278508&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2017)138

DO - 10.1007/JHEP10(2017)138

M3 - Article

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

M1 - 138

ER -