Studying Chaos in a Non-Chaotic System: Out-of-Time-Order-Correlators for the Classical Model of the Hydrogen Atom

For classical chaos to occur, the equation of motion for the system has to be non-linear; in contrast, the Schrodinger equation in quantum mechanics is a linear differential equation, begging the question of how chaos arises from non-chaotic origins. One lead the field of quantum chaos is pursuing is the out-of-time-order correlator (OTOC). The proposal is that if the OTOC of a given system (both classical and quantum) grows exponentially, then that system is chaotic. There are cases, however, where the OTOC grows exponentially for non-chaotic systems. I present one of those cases here where we have calculated the OTOC for the classical model of the hydrogen atom, finding that there is indeed exponential growth, and some other interesting findings we've found from this calculation.