Extracting classical Lyapunov exponent from one-dimensional quantum mechanics

Abstract

The commutator [x(t),p] in an inverted harmonic oscillator (IHO) in one-dimensional quantum mechanics exhibits remarkable properties. It reduces to a c-number and does not show any quantum fluctuations for arbitrary states. Related to this nature, the quantum Lyapunov exponent computed through the out-of-time-order correlator (OTOC) ⟨[x(t),p]2