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Journal of North China Electric Power University

Quantum effects of mesoscopic RLC circuit

Zhenjun Ding

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

On the condition that the electric charge takes discrete value,the finite differenc Schrodinger equation ofthemesoscopic RLC circuit is achieved.With a unitary transformation,the Schrodinger equation is transformed into the standard Mathieu equation in the generalized momentum presentation.The energy spectrum and the wave functions of the system are obtained.The average of currents and square of the current are calculated by using the WKM method.The results show the existence of the current.

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On the condition that the electric charge takes discrete value,the finite differenc Schrodinger equation ofthemesoscopic RLC circuit is achieved.With a unitary transformation,the Schrodinger equation is transformed into the standard Mathieu equation in the generalized momentum presentation.The energy spectrum and the wave functions of the system are obtained.The average of currents and square of the current are calculated by using the WKM method.The results show the existence of the current.
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 Schrodinger equation of.the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger 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 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.
Based on the fundamental fact that the electric charge takes discrete value,the finite-differenced Schrdinger equation of the mesoscopic LC circuit with a source is achieved.With a unitary transformation,the Schrdinger equation becomes the standard Mathieu equation.Using the WKBJ method,the energy spectrum and the wave functions of the system are obtained,the average of currents and square of the current are calculated,the results show the existence of the current fluctuation,which cause the noise in the circuits.
According to the charge discrete values,mesoscopic RLC circuit with a power source has been quantized based on the full quantum theory of the mesoscopic circuit.Thus,a systemetic finite-difference Schrdinger equation has been obtained.In representation,the form of Schrodinger equation has been transformed into the standard Mathieu equation.In the WKBJ approximation,the energy level distribution of Mesoscopic RLC Circuit with a Power Source has been obtained,and then the average of and 2 in the ground state has been calculated.The problem of quantum fluctuations in Mesoscopic RLC circuit with a power source has been solved by quantum statistical mechanics.
The importance of discreteness of electron charge for mesoscopic electric circuit is addressed. A quantization of the circuit in accord with the discreteness of electric charges is proposed, and a Schrödinger equation in ‘charge representation’ is obtained. The Schrödinger equation is turned to be Mathieu equation in ‘current representation’, the wavefunction and energy spectrum can be solved exactly. The WKB solutions of the energy levels for the ground state and the excited states are given.