Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator

Understand

We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos.

• The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator.
• We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold.
• The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature.