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Quantum Circuit Equation and Quantum Current of Mesoscopic Electron Resonator with Charge Discreteness

Cui Yuan-shun

Published Sep 26, 2007• 0 citations
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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.

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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 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.
On the basis of the charge discreteness, the inductance-coupling rnesoscopic circuit is quantized, the quantum loop equations in coupling form are given, and the energy spectrum is computed in charge representation. The results show that, taking account of the charge discreteness, it will make the quantum loop equations complicated, and the energy spectrum of the circuit is not only related with the circuit parameters, but depended on the quantization character of the charge and the undetermined phases.
On the basis of quantization of charge, the loop equations of quantum circuits are investigated by using the Heisenberg motion equation for a mesoscopic dissipation transmission line. On the supposition that the system has a symmetry under translation in charge space, the quantum current and the quantum energy spectrum in the mesoscopic transmission line are given by solving their eigenvalue equations. Results show that the quantum current and the quantum energy spectrum are not only related to the parameters of the transmission line, but also dependent on the quantized character of the charge obviously.
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.