Utilizing an Adaptive Earth Mover's Distance to Detect Quantum Chaos

The correspondence between classical chaos and quantum mechanics is not well understood and is an active area of research. One understudied definition of quantum chaos directly borrows from that of its classical counterpart– a quantum system that is characterized by a positive Lyapunov exponent describing the exponential rate of separation of trajectories with infinitesimally close initial conditions in phase space. Describing an exponential rate of separation of trajectories is a challenging problem in quantum mechanics, as quantum systems are described by their Wigner function rather than a single point in phase space. One metric commonly used to define distances between probability density distributions is the Earth Mover's Distance, a distance that can be reformulated as a transportation problem. In this presentation, we show calculations of the Earth Mover's Distance over time of prototypical quantum states. Additionally, we present an adaptive Earth Mover's Distance method to compute distances between Wigner functions as a method of detecting quantum chaos.