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

Acta Sinica Quantum Optica

The Quantum Loop Equation and the Energy Spectrum for the Capacitance Coupled Mesoscopic Circuit with Charge Discreteness

Zhou Huai-ling

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

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.

Related papers

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

Zhou Huai-ling

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.

Chinese Journal of Quantum Electronics•Jan 1, 2006•0 citations

The quantum Kirchhoff equation and quantum current and energy spectrum of a homogeneous mesoscopic dissipation transmission line

Cui Yuan-shun

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.

Chinese Physics•Oct 1, 2007•2 citations

Josephson junction in the quantum mesoscopic electric circuits with charge discreteness

Hassan Pahlavani

A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.

International Journal of Modern Physics B•Feb 22, 2018•2 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

THE PERSISTENT CURRENT ON A DRIVEN MESOSCOPIC RLC CIRCUIT

Hassan Pahlavani

The quantum theory for mesoscopic electric LC circuits with charge discreteness is briefly described. We take into account a resistance element (R) as an environment of the discrete-charge mesoscopic quantum LC circuit which is modeled by a Hamiltonian consisting of oscillators with continuous range of frequencies. Using a minimal coupling method, we investigate the quantum dynamics of this system. Hereby, the persistent current on a quantum damped L-design under the external potential source is obtained. Then, we write Heisenberg equations for a driven mesoscopic quantum RLC circuit with a dissipative term proportional to Ohmic damping and obtain persistent current on such a mesoscopic electric circuit.

International Journal of Modern Physics B•Jun 29, 2011•6 citations

The Quantum Fluctuations in the Dissipative Mesoscopic Circuit with the Charge Discreteness under Fock State

Hailan Jin, Cui Yuan-shun

On the basis of the charge quantization,the quantum fluctuations of the charge,the current and the energy in the dissipative mesoscopic circuit are calculated by the character of the minimum shift operator.The results show that,taking account of the charge discreteness,the quantum fluctuation of charge is zero under Fock state,but the fluctuations of the current and the energy aren't zero,which relate with charge quantization,Plank constant and the parameters of the circuits.

Journal of Huaiyin Teachers College•Jan 1, 2007•0 citations
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 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.
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.
A quantum mesoscopic electrical LC-circuit with charge discreteness including a Josephson junction is considered and a nonlinear Hamiltonian that describing the dynamic of such circuit is introduced. The quantum dynamical behavior (persistent current probability) is studied in the charge and phase regimes by numerical solution approaches. The time evolution of charge and current, number-difference and the bosonic phase and also the energy spectrum of a quantum mesoscopic electric LC-circuit with charge discreteness that coupled with a Josephson junction device are investigated. We show the role of the coupling energy and the electrostatic Coulomb energy of the Josephson junction in description of the quantum behavior and the spectral properties of a quantum mesoscopic electrical LC-circuits with charge discreteness.
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.
The quantum theory for mesoscopic electric LC circuits with charge discreteness is briefly described. We take into account a resistance element (R) as an environment of the discrete-charge mesoscopic quantum LC circuit which is modeled by a Hamiltonian consisting of oscillators with continuous range of frequencies. Using a minimal coupling method, we investigate the quantum dynamics of this system. Hereby, the persistent current on a quantum damped L-design under the external potential source is obtained. Then, we write Heisenberg equations for a driven mesoscopic quantum RLC circuit with a dissipative term proportional to Ohmic damping and obtain persistent current on such a mesoscopic electric circuit.