Adomian Decomposition Approach to Solve the Quantum Mesoscopic Nonlinear LC-circuits with Charge Discreetness

The quantum Hamitonian of a nonlinear mesoscopic LC-circuit include a nonlinear inductor and a linear capacitor with charge discreetness is introduced. An analytical function for quantum persistent current due to  the magnetic flux of such nonlinear electrical circuit is obtained by Adomian Decomposition Method (ADM). The nonlinear quantum ring is introduced and the quantum persistent current and the eigenvalues energy are found analytically. It is shown by numerical solution that the persistent current and eigenvalues energy are periodic functions of the magnetic flux with the fundamental parameter ( ),  which is a pure quantum characteristic.  In this paper, we proved for the first time that in a mesoscopic nonlinear quantum ring, similar a linear quantum ring, there is a quantized and periodic persistent current in terms of magnetic flux, which will attract attention in experience and technology.