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Journal of Zhengzhou University

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

Hong Li

Published Jan 1, 2007• 0 citations
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Abstract

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.

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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.
The quantum fluctuations of the voltage and the current in each branch of the quantized generalized mesoscopic RLC parallel circuit in squeezed vacuum state were studied.The factors affecting the fluctuations in each branch were also analyzed.The results show that the quantum fluctuations in each branch of the circuit in squeezed vacuum state are related to the factors which are the elements of the circuit,the parameters of the squeezed vacuum state and the time.All the quantum fluctuations of the voltage and the current in each branch of the circuit decay with time exponentially.The decay rates are related to the elements of the circuit only,not to the parameters of the squeezed vacuum state.The amplitude of the fluctuations at the initial stage depends on the elements of the circuit and the parameters of the squeezed vacuum state.
When the inelastic coherence length of the charge carrier reaches the Fermi wavelength,quantum effects in electronic devices and circuit should be taken into account.Due to the existence of finite environmental temperature and damped resistance,practical circuits are always working in damped thermal states at finite temperature.With the rapid development of nanotechnology and microeletronics,the quantum effects of mesoscopic circuit have become an active problem now.In this paper,mesoscopic series-parallel connection RLC circuit was quantized by the method of damped harmonic oscillator quantization.Quantum fluctuatioins of the current and voltage of each branch were studied by thermo-field dynamics(TFD) theory in thermal vacuum state,thermal coherent state and thermal squeezed state.The results show that the quantum fluctuations of the current and voltage of each branch are related to not only parameters of the circuit,but also squeezed coeficients,squeezed angle and envionmental temperature.Because of the existence of current Joule heat,environmental temperature and damped resistances,the fluctuations increase with the increasing of temperature and decay with time.The study of these quantum fluctuation is significant for the design of miniature circuits and the reduction of quantum noise.
By referring to the idea of dealing with damped harmonic oscillator in quantum mechanics,the mesoscopic parallel RLC circuit with dissipative capacitance branch circuit is quantized.On this basis,the quantum fluctuations of the voltage and current of each branch circuit in vacuum state are studied.The result shows that the quantum fluctuations of the voltage and current of each branch circuit are related with the parameters of the circuit elements,and decay according to exponent along with time,and that the attenuations of the quantum fluctuations are the same,but their coefficients are different,and that the quantum fluctuations of the voltage and current of each branch circuit are affected by the dissipative resistance.
The quantization of the generalized mesoscopic RLC parallel circuit,the quantum fluctuations of the current and the voltage of each branch in vacuum state were studied.The influences on the quantum fluctuations of the dissipative resistances in the inductance and capacitance branches were discussed.The results show that the quantum fluctuations in each branch are related to the parameters of the elements and decay with time.The quantum fluctuations in the two branches are influenced by the dissipative resistances both in the decaying factor and in the coefficients.They have the same behavior in the decaying factor but having difference in the coefficients.The quantum fluctuations of the voltage are affected by the dissipative resistances in the two branches,but the quantum fluctuations of the current are not affected by them when the values of the two dissipative resistances are same.
Mesoscopic damped mutual inductance coupled double resonance RLC circuit is quantized by the method of damped harmonic oscillator quantization and linear transformation. The energy levels of this circuit are given. By thermo-field dynamics (TFD), the quantum fluctuations of the current and voltage of each loop are researched in the thermal vacuum state, thermal coherent state and thermal squeezed state. It is shown that the quantum fluctuations of the current and voltage are related not only to the circuit inherent parameter and coupled magnitude of mutual inductance, but also squeezed coefficients, squeezed angle, environmental temperature and damped resistance. Furthermore, because of environmental temperature and damped resistance, the quantum fluctuations increase with the increase of temperature and decay along with time.