In the framework of free electron approximation,the analytical results of persistent currents and energy spectra of one-dimensional spin-dependent mesoscopic ring driven by time-dependent electric fields have been given.

Based on an exactsecond guantized Hamiltonian of non-interacting electron gas in the mesoscopic ring mixed withAB,AC effect,analytic solutions for energy eigenvalues, the persistent current and Dersistentspin curreut are obtained It is shown that AC effect is extremely important for electrons in somesemiconductors applied with intense electric field.

We obtain the transmittance in a one-dimensional mesoscopic ring array with the help of quantum waveguide theory.

The supercurrent of ballistic mesoscopic rings threaded by time dependent flux is discussed by making use of the single valued wave function of Aharonov Bohm problem.

For the mesoscopic metal ring system in external magnetic field,supposing the system has a symmetry under translation in charge space,the quantum current and the quantum energy spectrum in mesoscopic metal ring are given by solving thire eigenvalue equations;and the quantum fluctuations of the current and the energy have been calculated by the character of the minimum shift operator.

For one-dimensional mesoscopic metal rings system in external magnetic field, supposing the system has a symmetry under translation in charge space, the quantum current relation in mesoscopic metal rings is given by solving the eigenvalue equation of the current, the property of quantum current have been investigated and analysed.

On the basis of the charge discreteness,the quantum fluctuations fo the charge,current and energy in the mesoscopic metal dual rings are calculated by the minimum shift operator.

Based on the discreteness of electric charge, the influences of an external magn etic filed on the persistent current of the mesoscopic coupling metallic rings a re investigated.