Quantum and classical chaos of a two-spinless-fermion system in a quantum wire

We study the classical and quantum dynamics of two spinless fermions confined in a quantum wire with a repulsive or an attractive Coulomb interaction. The interaction induces irregular dynamics in the classical mechanics, which reflects on the quantum properties of the system in the energy level statistics (the signatures of quantum chaos). We especially investigate the close correspondence between classical and quantum chaos. The classical dynamics studied has a scaling property, which the quantum counterpart does not have. However, we demonstrate that the energy level statistics implies the existence of a corresponding scaling property, even in the quantum system. Instead of an ordinary maximum Lyapunov exponent (MLE), we introduce a modified MLE, which is shown to be a suitable measure of the chaotic irregularity in the classical system studied. We show that the tendency of the energy dependence of the Brody parameter, which characterizes the energy level statistics in the quantum system, is consistent with that of the modified MLE.