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

Journal of Guangxi Academy of Sciences

Five Quantization Methods of the Mesoscopic RLC Series Circuit

Qingyi Yang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The mesoscopic RLC series circuit are quantized by five different ways which are the forced damp harmonic vibration,the construct the Hamiltonian and associated canonical transformation,the damped harmonic vibration canonical transformation,the construct the Hamiltonian and associated unitary transformation and the inner construction of the resistance are summarized.The quantum fluctuations of the charge,the current and their products are analyzed when the system in the vacuum state.The different results from the same circuit quantized by different methods are due to the different chice of the Hamiltonion of the system.

Related papers

The Quantum Fluctuations of Mesoscopic Damped Mutual Capacitance Coupled Double Resonance RLC Circuit

Xing-Lei Xu

Mesoscopic damped double resonance mutual capacitance coupling circuit is quantized by the method of damped harmonic oscillator quantization.Hamiltonian is diagonalized by unitary transformation.The energy spectra of this circuit are given.The quantum fluctuations of the charge and current of each loop in Fock state and vacuum state are researched.

Journal of Jiangxi Normal University•Jan 1, 2006•0 citations

Quantum Wavefunctions and Fluctuations of Mesoscopic RLC Circuit

Ji‐Suo Wang, Tang-Kun Liu, Mingsheng Zhan

The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as well as the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.

Chinese Physics Letters•Jul 1, 2000•17 citations

Quantum Fluctuation in Mesoscopic RLC Circuit

Shou Zhang

WT5BZ]The damped harmonic Hamiltonian is infered from harmonic Hamiltonian, by introducing the canonical transformation. And the quantum fluctuation of charge and current in the mesoscopic circuit in squeezed states are strdied, too. [WT5HZ]

Acta Sinica Quantum Optica•Jan 1, 2001•0 citations

Quantum fluctuations of charge and current in RLC circuit

Wang Zhong-chen, Guo Zheng-ping

Starting from equation of motion of the active RLC circuit,we adopt the technique of the unitary transformation,transform the charge and current into the unitary variable and then have the quantization.By making use of standard transformation,we try to solve the time equation.For the application,quantum fluctuations of charge and the current in the mesoscopic circuit in the harmonic oscillator state are studied,result is analyzed and discussed.

Journal of Qingdao Technological University•Jan 1, 2006•0 citations

Quantum Fluctuations of Mesoscopic Series-parallel Connection RLC Circuit in Excitation State of the Squeezed Vacuum State

Hong Li

Mesoscopic series-parallel connection RLC circuit is quantized by the method of damped harmonic oscillator operation.On this basic theory,quantum fluctuations of the current and voltage of each branch in excitation state of the squeezed vacuum state,squeezed vacuum state and vacuum state are studied.The result shows that the quantum fluctuations of the current and voltage of each branch are related with not only parameter of the circuit element,but also quantum number of excitation,squeezed coefficients and squeezed angle.These fluctuations decay with time because of damped resistance.

Journal of Zhengzhou University•Jan 1, 2007•0 citations

On the Quantization of Parallel Mesoscopic RLC Circuitand the Quantum Fluctuations

Wu Yun-Yi, Lei Min-Sheng, Mingyu Chen

A method of quantizing the active parallel mesoscopic RLC circuits developed,and the quantum fluctuations of currents and voltages in the parallel mesoscopic RLC circuits in the vacuum state,especially the influences of resistance on the quantum fluctuation are investigted.

Jiangxi kexue•Jan 1, 2005•0 citations
The mesoscopic RLC series circuit are quantized by five different ways which are the forced damp harmonic vibration,the construct the Hamiltonian and associated canonical transformation,the damped harmonic vibration canonical transformation,the construct the Hamiltonian and associated unitary transformation and the inner construction of the resistance are summarized.The quantum fluctuations of the charge,the current and their products are analyzed when the system in the vacuum state.The different results from the same circuit quantized by different methods are due to the different chice of the Hamiltonion of the system.
The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as well as the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.
Mesoscopic series-parallel connection RLC circuit is quantized by the method of damped harmonic oscillator operation.On this basic theory,quantum fluctuations of the current and voltage of each branch in excitation state of the squeezed vacuum state,squeezed vacuum state and vacuum state are studied.The result shows that the quantum fluctuations of the current and voltage of each branch are related with not only parameter of the circuit element,but also quantum number of excitation,squeezed coefficients and squeezed angle.These fluctuations decay with time because of damped resistance.