Abstract
The open electron resonator is a mesoscopic device that has attracted considerable attention due to its remarkable behavior: conductance oscillations. In this paper, using an improved quantum theory to mesoscopic circuits developed recently by Li and Chen, the mesoscopic electron resonator is quantized based on the fundamental fact that the electric charge takes discrete value. With presentation transformation and unitary transformation, the Schrödinger equation becomes an standard Mathieu equation. Then, the detailed energy spectrum and wave functions in the system are obtained, which will be helpful to the observation of other characters of electron resonator. The average of currents and square of the current are calculated, the results show the existence of the current fluctuation, which causes the noise in the circuits, the influence of inductance to the noise is discussed. With the results achieved, the stability characters of mesoscopic electron resonator are studied firstly, these works would be benefit to the design and control of integrate circuit.
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