Out-of-time-order correlator in coupled harmonic oscillators

Understand

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.