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

Chinese Physics

Quantum fluctuation of mesoscopic distributed parameter circuits

Haimei Luo, Liu Gang, Lin Xu, Yinghua Ji

Published Sep 28, 2004• 5 citations
Publisher

Abstract

Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for a non-dissipative distributed parameter circuit (a uniform transmission line). Quantum fluctuations of charge and current in the vacuum state are investigated by adopting the canonical transformation and unitary transformation method. Our results indicate that in distributed parameter circuits, quantum fluctuations, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.

DOI
10.1088/1009-1963/13/10/034

Related papers

Density Matrix for Mesoscopic Distributed Parameter Circuits

Yinghua Ji, Wang Qi, Haimei Luo +1 more

Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix ρ( q , q ′,β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T . The higher the temperature is, the stronger quantum noise the circuit exhibits.

Communications in Theoretical Physics•Mar 1, 2005•1 citation

THE QUANTIZATION OF A MESOSCOPIC TRANSMISSION LINE WITH THE DISCRETENESS OF ELECTRIC CHARGE

Yinghua Ji

The quantization of a mesoscopic transmission line in accordance with the discreteness of electric charges is proposed under the Born–Von-Karmann periodic boundary condition. The finite-difference Schrödinger equation of the circuit has been obtained in charge representation, and the Schrödinger equation is transformed into Mathieu equation in current representation. The wavefunction and energy spectrum can be solved by adopting the canonical transformation and unitary transformation method. Our results indicate that in the transmission line, quantum fluctuation of currents, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.

International Journal of Modern Physics B•Jun 20, 2009•1 citation

Density Matrix for Mesoscopic Distributed Parameter Circuits

JIYing-Hua, WangQi, LUOHai-Mei +1 more

Under the Born-von-Karmann periodic boundary condition, we propose a quantization scheme for nondissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix p(q, q',β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.

理论物理通讯：英文版•Jan 1, 2005•0 citations

QUANTUM FLUCTUATION IN THERMAL VACUUM STATE FOR MESOSCOPIC DISTRIBUTED PARAMETER CIRCUITS

Yinghua Ji, Haimei Luo, Yi-Fan Wang +1 more

In this paper we consider a non-dissipative distributed parameter circuit at a finite temperature T. We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation. Thermal field dynamic is used in our discussion. It is shown that distributing parameter circuits and quantum fluctuations, which also have distributing properties, are related to both the circuit parameters and the positions and the model of signals and temperature T. The higher the temperature, the more quantum noise the circuit exhibits. The research will be helpful to miniaturize intergreate circuits and electric components. It will be also significant for the futher study of the qualitities of mesoscopic system.

International Journal of Modern Physics B•Apr 20, 2005•2 citations

The quantization of a mesoscopic dissipation transmission line

Wang Zhong-Chun, 盐城师范学院物理系,盐城 224002

Starting from the classical equation of motion a dissipation transmission line,the mesoscopic dissipation transmission line is quantized.The quantum effects of the line under excited coherent states are investigated.The results indicate that the quantum fluctuations of the line are not only determined by the circuit parameter and the states of the circuit,but also dependent on the position of the line.

Acta Physica Sinica•Jan 1, 2003•2 citations

Quantum fluctuations of dissipative mesoscopic RLC series and parallel circuit in thermal vacuum state

Kong Ling-ji

By using canonical quantization method of damped harmonic oscillator,the quantum of dissipative mesoscopic RLC series and parallel circuit was realized in this paper.And on this basis,the quantum fluctuations of charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state which based on thermal field dynamics theory were also studied through this research methods.The results show that charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state respectively exist quantum fluctuations.And the quantum fluctuations and quantum fluctuations plot not only depend on device parameters in the circuit,but also depend on time and temperature.

Journal of Northeast Normal University•Jan 1, 2015•0 citations
Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for a non-dissipative distributed parameter circuit (a uniform transmission line). Quantum fluctuations of charge and current in the vacuum state are investigated by adopting the canonical transformation and unitary transformation method. Our results indicate that in distributed parameter circuits, quantum fluctuations, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.
Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix ρ( q , q ′,β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T . The higher the temperature is, the stronger quantum noise the circuit exhibits.
The quantization of a mesoscopic transmission line in accordance with the discreteness of electric charges is proposed under the Born–Von-Karmann periodic boundary condition. The finite-difference Schrödinger equation of the circuit has been obtained in charge representation, and the Schrödinger equation is transformed into Mathieu equation in current representation. The wavefunction and energy spectrum can be solved by adopting the canonical transformation and unitary transformation method. Our results indicate that in the transmission line, quantum fluctuation of currents, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.
Under the Born-von-Karmann periodic boundary condition, we propose a quantization scheme for nondissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix p(q, q',β). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.
In this paper we consider a non-dissipative distributed parameter circuit at a finite temperature T. We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation. Thermal field dynamic is used in our discussion. It is shown that distributing parameter circuits and quantum fluctuations, which also have distributing properties, are related to both the circuit parameters and the positions and the model of signals and temperature T. The higher the temperature, the more quantum noise the circuit exhibits. The research will be helpful to miniaturize intergreate circuits and electric components. It will be also significant for the futher study of the qualitities of mesoscopic system.
By using canonical quantization method of damped harmonic oscillator,the quantum of dissipative mesoscopic RLC series and parallel circuit was realized in this paper.And on this basis,the quantum fluctuations of charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state which based on thermal field dynamics theory were also studied through this research methods.The results show that charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state respectively exist quantum fluctuations.And the quantum fluctuations and quantum fluctuations plot not only depend on device parameters in the circuit,but also depend on time and temperature.