Entangled state representation for mesoscopic persistent current ring and its phase-angular momentum

The entangled state representation was establish,in which the phase operator and the angular momentum operator have been applied, to realize the phase-angular momentum quantization of mesoscopic persistent current ring (MPCR) , and derive its energy spectrum. In addition,it was revealed that the ascending/lowering of angular momentum corresponds to the currents increase/decrease through angular momentum representation for the persistent current ring.