Abstract: On the basis of charge discreteness,the properties of quantum current in a mesoscopic electron resonator are investigated by the minimum shift operator.Quantum Kirchhoff’s equation,the current relation,and the fluctuations of current are given.The results show that when charge quantization is taken into account,the charge in the resonator has the characteristic of quantum vibration;the quantum current and the fluctuation are related to the charge quantum and Planck constant,respectively,and the size is determined by the self-inductance of the system.

Key words: mesoscopic electron resonator, charge quantization, quantum Kirchhoff’s equation, quantum current