  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.
