Distribution of the ratio of consecutive level spacings for different symmetries and degrees of chaos
Distribution of the ratio of consecutive level spacings for different symmetries and degrees of chaos
Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\ensuremath{\equiv}P(r;\ensuremath{\beta})$, where $\ensuremath{\beta}\ensuremath{\in}[0,+\ensuremath{\infty})$ is a generalized Dyson index, that describes the eigenlevel statistics of a quantum system characterized by different symmetries and degrees …