Transition of Spectral Statistics of a Spin-1/2 Coupled Quartic Oscillators from GSE to Integrable Regime

Abstract

A large amount of work has been done in the past decades to understand quantum chaos. Most work has been concentrated on a spinless particle in two dimensions, which provides the simplest and the most fundamental knowledge of quantum chaotic systems (see Ref.1, and references therein). In this work, we study the system of a spin-1/2 particle in three dimensions, which is also essential for physics. By choosing parameters, our system has three kinds of chaotic limits, which correspond to the Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble(GUE) and the Gaussian Symplectic Ensemble(GSE). However, the intermediate regime between the integrable and the GSE (or the GUE) class has been scarcely studied. In addition to the nearest neighbor level spacing distribution(NNSD), We also adopt the mode fluctuation distribution(MFD), which was introduced for the signature of chaoticity. Half-integer spin and three dimensions lead us to the chaotic system that is not the GOE class. In this work, spectral statistics of the GOE, the GSE, the integrable classes and their intermediate ones are studied.