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Chinese Journal of Quantum Electronics

Quantum loop equation and the energy spectrum of the inductance-coupling mesoscopic circuit

Zhou Huai-ling

Published Jan 1, 2006• 0 citations
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Abstract

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.

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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.
The quantum theory for the dual LC mesoscopic coupled electric circuit with charge discreteness is briefly described. The quantum Kirchoff's moving equation, and energy spectrum of the mesoscopic coupled circuit is given under the non-interaction Hamilton digenstate vectors. The results show that, taking account of the charge discreteness, a evident change occurred for the equation of mesoscopic circuit, and the energy spectrum of the circuit are not only related with the circuit parameters, but depended the quantization character of the charge.
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.
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.
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.