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 |
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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 journal › Article
}
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
AN - SCOPUS:85032278508
VL - 2017
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 10
M1 - 138
ER -