Out-of-time-order correlators in quantum mechanics

Koji Hashimoto, Keiju Murata, Ryosuke Yoshii

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 languageEnglish
Article number138
JournalJournal of High Energy Physics
Volume2017
Issue number10
DOIs
Publication statusPublished - 2017 Oct 1

Fingerprint

correlators
quantum mechanics
boxes
chaos
harmonic oscillators
energy spectra

Keywords

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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

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

In: Journal of High Energy Physics, Vol. 2017, No. 10, 138, 01.10.2017.

Research output: Contribution to journalArticle

Hashimoto, Koji ; Murata, Keiju ; Yoshii, Ryosuke. / Out-of-time-order correlators in quantum mechanics. In: Journal of High Energy Physics. 2017 ; Vol. 2017, No. 10.
@article{a10f402a1e1d4e42aa71428a4b7ffee8,
title = "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 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.",
keywords = "AdS-CFT Correspondence, Black Holes, Models of Quantum Gravity",
author = "Koji Hashimoto and Keiju Murata and Ryosuke Yoshii",
year = "2017",
month = "10",
day = "1",
doi = "10.1007/JHEP10(2017)138",
language = "English",
volume = "2017",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",
number = "10",

}

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 -