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Journal of Huaiyin Teachers College

The Quantum Current and Energy Spectrum in Mesoscopic Metal Ring and the Quantum Fluctuations under External Magnetic Field

Cui Yuan-shun

Published Jan 1, 2006• 0 citations
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Abstract

For the mesoscopic metal ring system in external magnetic field,supposing the system has a symmetry under translation in charge space,the quantum current and the quantum energy spectrum in mesoscopic metal ring are given by solving thire eigenvalue equations;and the quantum fluctuations of the current and the energy have been calculated by the character of the minimum shift operator.The properties of the quantum current and the quantum energy spectrum have been investigated,and the effects of the parameters on the quantum fluctuations are analysed.The results show that the quantum current and the quantum energy spectrum are not only related with the external magnetic field and the parameters of the mesoscopic metal ring,but depended on the quantization character of the charge evidently.

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For the mesoscopic metal ring system in external magnetic field,supposing the system has a symmetry under translation in charge space,the quantum current and the quantum energy spectrum in mesoscopic metal ring are given by solving thire eigenvalue equations;and the quantum fluctuations of the current and the energy have been calculated by the character of the minimum shift operator.The properties of the quantum current and the quantum energy spectrum have been investigated,and the effects of the parameters on the quantum fluctuations are analysed.The results show that the quantum current and the quantum energy spectrum are not only related with the external magnetic field and the parameters of the mesoscopic metal ring,but depended on the quantization character of the charge evidently.
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 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.
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 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.
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.