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Journal of Southwest Jiaotong University

Quantum Effects in Mesoscopic RLC Circuit under Eigenstate of Ladder Operator

Zhou Huai-ling

Published Jan 1, 2009• 0 citations
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Abstract

To investigate the factors influencing quantum fluctuations,the quantum fluctuations of charge,current and energy in a mesoscopic RLC circuit were calculated in a new Fock space defined by the charge operator using the character of the minimum shift operator based on charge quantization. The results show that,taking account of charge discreteness,the quantum fluctuation of current is zero under the eigenstate of ladder operator,and the fluctuations of charge and energy are determined by charge quantum,Planck constant and state parameters. In addition,the fluctuation of energy depends also on RLC parameters of the circuit,the power source and the external magnetic field.

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•Jan 1, 2007•0 citations
To investigate the factors influencing quantum fluctuations,the quantum fluctuations of charge,current and energy in a mesoscopic RLC circuit were calculated in a new Fock space defined by the charge operator using the character of the minimum shift operator based on charge quantization. The results show that,taking account of charge discreteness,the quantum fluctuation of current is zero under the eigenstate of ladder operator,and the fluctuations of charge and energy are determined by charge quantum,Planck constant and state parameters. In addition,the fluctuation of energy depends also on RLC parameters of the circuit,the power source and the external magnetic field.
On the basis of the charge quantization,the quantum fluctuations of the mesoscopic LC circuit under the eigenstate of ladder operator are calculated,and the effects of the parameters on the fluctuations are investigated.The results show that taking account of the charge discreteness,the quantum fluctuations of the charge and the energy aren't zero,related with the charge quantum and the state parameters respectively;In addition,the quantum fluctuations of the energy are determined by the parameters of the circuit.
In the inductance-coupling mesoscopic circuit,by taking account of the charge discreteness,a method for calculating quantum effects is proposed in the new Fock space that is formed by the eigenstate of charge operator.In this method,by introducting the minimum shift operator,the system Hamilton and the physics current are expressed according to the charge operator and the ladder operator,and the quantum fluctuations of the charge,current and energy are calculated directly by the character of the ladder operator.The obtained results are related with self-inductance closely.In designing the quantum circuit and the nanoelectroic devices,the considerable factors are given for the quantum noise reduction.
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.
On the basis of the charge quantization, The quantum fluctuations of the charge, current and energy in the mesoscopic metal ring are calculated by the character of the minimum shift operatorQ∧, the effects of the parameters on the quantum fluctuations are investigated. The results show that, taking account of the charge discreteness, the quantum fluctuations of the charge, energy are not zero under the coherent state, related with the charge quantum and the parameters of the coherent state respectively. In addition, the quantum fluctuations of energy are also determined by the inductance of the mesoscopic metal ring, the external magnetic flux and its time variable rate.