Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Quantum Effects of Mesoscopic Inductance and Capacity Coupling Circuits

Jianxin Liu, Zhan-Yuan Yan, Song Yong-Hua

Published Jun 1, 2006• 11 citations
Publisher

Abstract

Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finite-difference Schrödinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrödinger equation can be divided into two Mathieu equations in representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.

DOI
10.1088/0253-6102/45/6/032

Related papers

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 College•Jan 1, 2006•0 citations

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 Physics•Dec 1, 2005•8 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, 2005•0 citations

Quantum Theory for Mesoscopic Electric Circuits and Its Applications

You‐Quan Li, Bin Chen

This talk is assumed to exhibit an overview of the quantum theory for mesoscopic electric circuits and some of its further developments. In the theory the importance of the discreteness of electronic charge in mesoscopic electric circuit is addressed. The mesoscopic LC-design is quantized in accord with the charge discreteness. The uncertainty relation for electric charge and current is given. Because the stationary Schrödinger equation is turned to be Mathieu equation in $p$-representation, the wave function and energy spectrum is formally solved. As further applications, the persistent current is obtained by considering the mesoscopic ring as a pure L-design. The Coulomb blockade phenomenon occurs when applying the theory to the pure C-design. Concerning the time evolution of the states for mesoscopic electric circuit, we are able to study it by the method of characteristics. In order to study the dissipative effect in the circuit, we use density-matrix formulation. In this formulation, several type of ``off diagonal'' dissipations are expected to be discussed.

arXiv:cond-mat/9907171•Jul 12, 1999•1 citation

Improved Quantization Method of Coupled Circuits in Charge Discrete Space

Jinying Ma, Weiran Zhao, Weilin Wang +1 more

A quantum theory of mesoscopic circuits, based on the discreteness of electric charges, was recently proposed. However, it is not applied widely, mainly because of the difficulty of the mathematical solution to the finite-difference Schrödinger equation. In this paper, we propose an improved perturbation method to calculate Schrödinger equations of the inductance and capacity coupling mesoscopic circuit. With a unitary transformation, the finite differential Schrödinger equation of the system is divided into two equations in generalized momentum representation. The concrete value of the parameter in circuits is important to solving the equation. Both the perturbation method suitable case and the improved perturbation method suitable case, the wave functions, and energy level of the system are achieved. As an application, the current fluctuations are calculated and discussed. The improved mathematical method would be helpful for the popularization of the quantum circuits theory.

Mathematics•Nov 28, 2024•1 citation

Quantum effects in inductance coupled mesoscopic circuit at excited coherent states

Cai Shao-Hong, Jinping Kang, Zhang Yuqiang

Starting from the classical movement equation of a non-dissipative inductance coupled mesoscopic circuit,the circuit is quantized by using linear transformation method,and the quantum fluctuations of currents and charges at excited coherent states are calculated.The results show that the average and square average of current and charge of each loop are not zero without power,i.e.,there exist quantum fluctuations. And the fluctuations are not only determined by the loop parameters,but also related to another loop's parameters and coupled inductance parameters.The quantum fluctuations in two circuits are relevant,and obviously depend on the state parameters of circuits,i.e.,parameters of particle count states and coherent states.

Chinese Journal of Quantum Electronics•Jan 1, 2011•0 citations
Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finite-difference Schrödinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrödinger equation can be divided into two Mathieu equations in representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.
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.
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.
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.
This talk is assumed to exhibit an overview of the quantum theory for mesoscopic electric circuits and some of its further developments. In the theory the importance of the discreteness of electronic charge in mesoscopic electric circuit is addressed. The mesoscopic LC-design is quantized in accord with the charge discreteness. The uncertainty relation for electric charge and current is given. Because the stationary Schrödinger equation is turned to be Mathieu equation in ppp-representation, the wave function and energy spectrum is formally solved. As further applications, the persistent current is obtained by considering the mesoscopic ring as a pure L-design. The Coulomb blockade phenomenon occurs when applying the theory to the pure C-design. Concerning the time evolution of the states for mesoscopic electric circuit, we are able to study it by the method of characteristics. In order to study the dissipative effect in the circuit, we use density-matrix formulation. In this formulation, several type of ``off diagonal'' dissipations are expected to be discussed.
A quantum theory of mesoscopic circuits, based on the discreteness of electric charges, was recently proposed. However, it is not applied widely, mainly because of the difficulty of the mathematical solution to the finite-difference Schrödinger equation. In this paper, we propose an improved perturbation method to calculate Schrödinger equations of the inductance and capacity coupling mesoscopic circuit. With a unitary transformation, the finite differential Schrödinger equation of the system is divided into two equations in generalized momentum representation. The concrete value of the parameter in circuits is important to solving the equation. Both the perturbation method suitable case and the improved perturbation method suitable case, the wave functions, and energy level of the system are achieved. As an application, the current fluctuations are calculated and discussed. The improved mathematical method would be helpful for the popularization of the quantum circuits theory.
Starting from the classical movement equation of a non-dissipative inductance coupled mesoscopic circuit,the circuit is quantized by using linear transformation method,and the quantum fluctuations of currents and charges at excited coherent states are calculated.The results show that the average and square average of current and charge of each loop are not zero without power,i.e.,there exist quantum fluctuations. And the fluctuations are not only determined by the loop parameters,but also related to another loop's parameters and coupled inductance parameters.The quantum fluctuations in two circuits are relevant,and obviously depend on the state parameters of circuits,i.e.,parameters of particle count states and coherent states.