Out-of-time-order correlators as a measure of quantum chaos for sinai, cardioid and diamond billiards

Abstract

The field of quantum chaos studies how the chaotic dynamics of a classical system manifest in its quantum counterpart. Various indicators and measures of classical chaos have been discovered, such as the classical Lyapunov exponent, that allow us to distinguish and analyze chaos in classical systems. However, the same cannot be said for quantum chaos. Measures of quantum chaos are few and far between, and the ones that have been found are not well understood. One such measure is the out-of-time-order correlator (OTOC). In this thesis, we employ out-of-time-order correlators to study quantum chaos in various billiard systems, and try to find correlations between the classical and quantum dynamics of these systems.