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Journal of Zhengzhou University

Study of Quantum Effects of Mesoscopic Circuit with an Electrical Source Using the Scheme of Gauss Propagator

Xing-Lei Xu

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The time evolvement of quantum state is studied by the scheme of Gauss propagator and Louisell's common canonical quantization for mesoscopic RLC circuit.Moreover,the formulaes of time evolvement wave function and transition probability of quantum state of this circuit are proposed.It is more significant to quantitative analysis quantum character of mesoscopic circuit.

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The time evolvement of quantum state is studied by the scheme of Gauss propagator and Louisell's common canonical quantization for mesoscopic RLC circuit.Moreover,the formulaes of time evolvement wave function and transition probability of quantum state of this circuit are proposed.It is more significant to quantitative analysis quantum character of mesoscopic circuit.
In this paper, mesoscopic RLC circuit with source is studied with Feynman's path integral method. Resistance and source in the circuits make the quantization process rather complicated. To solve the problem, fluctuation analysis method is proposed to calculate the path integral propagator. Furthermore, the wave function and quantum fluctuation of the system are obtained, and time evolution characters of the system are discussed. The methods used in the paper would be helpful to the application of mesoscopic quantum theory.
The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrödinger equation of the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrödinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.
The quantum wave function of mesoscopic RLC circuit with power source is obtained by the method of representational transformation, and with the wave function, the quantum fluctuation of the mesoscopic circuit was obtained. Meanwhile, the quantum effect of mesoscopic circuit with power source is investigated using the double wave function. By comparing between two kinds of methods, we confirm that the fluctuation is connected with the state of a circuit. This can be seen from the method of double wave function. The average values of ensemble solved by double wave function are just the expected values solved by the method of representational transformation.