Journal of Cangzhou Normal University

Quantum Statistical Mechanics and Quantum Fluctuations with a Power Source in a Mesoscopic RLC Circuit

Fang Ming

Published Jan 1, 2012• 0 citations

Abstract

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.

Related papers

Quantum Effect in the Mesoscopic RLC Circuits with a Source

Jianxin Liu, Zhan-Yuan Yan

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.

Communications in Theoretical PhysicsDec 1, 20058 citations

Quantum Effect in the Mesoscopic RLC Circuits with a Source

Liu, Jian-Xin, Yan yan +1 more

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.

理论物理通讯：英文版Jan 1, 20050 citations

Quantum Effect in the Mesoscopic RLC Circuits

GU Lian-zhong

Based on the fundamental fact that the electric charge takes discrete value,the Schrdinger finite-differenced equation of the mesoscopic RLC circuit with a source is achieved.With a unitary transformation,the Schrdinger equation becomes the standard Mathieu equation.Using method of series expansion,the energy spectrum and the wave functions of the system are obtained.

Journal of Hebei UniversityJan 1, 20090 citations

Quantum Effect in the Mesoscopic LC Circuits with a Source

Zhan-Yuan Yan

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.

Journal of Hebei UniversityJan 1, 20070 citations

The Coulomb Blockade and Quantum Fluctuations of Mesoscopic Capacity Coupling Circuits

LI Ling-duan

Using the quantum theory for a mesoscopic circuit based on the discreteness of electric charges, the finite-differenced Schrodinger equation of the non-dissipative mesoscopic capacity coupling circuit are achieved. The quantum effect not only comes from the quanumnization of circuit but also that of charge. Only after the properties of charge quanumnization is considered can the Coulomb blockade effect of a mesoscopic circuit be discussed. The Schrodinger equation can be divided into two Mathieu equations in p-representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. And the fluctuations are the main noise sources of quantum in the mesoscopic circuit.

Journal of Tangshan Teachers CollegeJan 1, 20060 citations

Quantum wave function and double-wavedescription of mesoscopic RLC circuit with a power source

Su Wenhui

The quantum wave function of mesoscopic RLC circuit with power source is obtained by the method of representational transformation, and with the wave function, the quantum fluctuation of the mesoscopic circuit was obtained. Meanwhile, the quantum effect of mesoscopic circuit with power source is investigated using the double wave function. By comparing between two kinds of methods, we confirm that the fluctuation is connected with the state of a circuit. This can be seen from the method of double wave function. The average values of ensemble solved by double wave function are just the expected values solved by the method of representational transformation.

Chinese Journal of Quantum ElectronicsJan 1, 20040 citations