Out-of-time-order correlator in coupled harmonic oscillators
- URL: http://arxiv.org/abs/2004.04381v2
- Date: Mon, 27 Apr 2020 06:09:11 GMT
- Title: Out-of-time-order correlator in coupled harmonic oscillators
- Authors: Tetsuya Akutagawa, Koji Hashimoto, Toshiaki Sasaki, Ryota Watanabe
- Abstract summary: We numerically observe that the thermal OTOC grows exponentially in time.
The exponential growth is certified because the growth exponent (quantum Lyapunov exponent) of the thermal OTOC is well matched with the classical Lyapunov exponent.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Exponential growth of thermal out-of-time-order correlator (OTOC) is an
indicator of a possible gravity dual, and a simple toy quantum model showing
the growth is being looked for. We consider a system of two harmonic
oscillators coupled nonlinearly with each other, and numerically observe that
the thermal OTOC grows exponentially in time. The system is well-known to be
classically chaotic, and is a reduction of Yang-Mills-Higgs theory. The
exponential growth is certified because the growth exponent (quantum Lyapunov
exponent) of the thermal OTOC is well matched with the classical Lyapunov
exponent, including their energy/temperature dependence. Even in the presence
of the exponential growth in the OTOC, the energy level spacings are not
sufficient to judge a Wigner distribution, hence the OTOC is a better indicator
of quantum chaos.
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