Statistical properties of antisymmetrized molecular dynamics for non-nucleon-emission and nucleon-emission processes

Statistical properties of antisymmetrized molecular dynamics (AMD) are classical in the case of nucleon-emission processes, while they are quantum mechanical for the processes without nucleon emission. In order to understand this situation, we first clarify that there coexist mutually opposite two statistics in the AMD framework: One is the classical statistics of the motion of wave packet centroids and the other is the quantum statistics of the motion of wave packets which is described by the AMD wave function. We prove the classical statistics of wave packet centroids by using the framework of the microcanonical ensemble of the nuclear system with a realistic effective two-nucleon interaction. We show that the relation between the classical statistics of wave packet centroids and the quantum statistics of wave packets can be obtained by taking into account the effects of the wave packet spread. This relation clarifies how the quantum statistics of wave packets emerges from the classical statistics of wave packet centroids. It is emphasized that the temperature of the classical statistics of wave packet centroids is different from the temperature of the quantum statistics of wave packets. We then explain that the statistical properties of AMD for nucleon-emission processes are classical because nucleon-emission processes in AMD are described by the motion of wave packet centroids. We further show that when we improve the description of the nucleon-emission process so as to take into account the momentum fluctuation due to the wave packet spread, the AMD statistical properties for nucleon-emission processes change drastically into quantum statistics. Our study of nucleon-emission processes can be conversely regarded as giving another kind of proof of the fact that the statistics of wave packets is quantum mechanical while that of wave packet centroids is classical.