Out-of-time-order correlator in coupled harmonic oscillators
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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- August 2020
- DOI:
- 10.1007/JHEP08(2020)013
- arXiv:
- arXiv:2004.04381
- Bibcode:
- 2020JHEP...08..013A
- Keywords:
-
- Gauge-gravity correspondence;
- Black Holes;
- Models of Quantum Gravity;
- High Energy Physics - Theory;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics;
- Nonlinear Sciences - Chaotic Dynamics;
- Quantum Physics
- E-Print:
- 27 pages, 14 figures. v2: analysis of level statistics improved, references and comments added