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Natural Science Journal of Xiangtan University

Quantum Fluctuations of the Mesoscopic LC Circuit under the Eigenstate of Ladder Operator in New Fock Space

Cui Yuan-shun

Published Jan 1, 2007• 0 citations
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Abstract

On the basis of the charge quantization,the quantum fluctuations of the mesoscopic LC circuit under the eigenstate of ladder operator are calculated,and the effects of the parameters on the fluctuations are investigated.The results show that taking account of the charge discreteness,the quantum fluctuations of the charge and the energy aren't zero,related with the charge quantum and the state parameters respectively;In addition,the quantum fluctuations of the energy are determined by the parameters of the circuit.

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On the basis of the charge quantization,the quantum fluctuations of the mesoscopic LC circuit under the eigenstate of ladder operator are calculated,and the effects of the parameters on the fluctuations are investigated.The results show that taking account of the charge discreteness,the quantum fluctuations of the charge and the energy aren't zero,related with the charge quantum and the state parameters respectively;In addition,the quantum fluctuations of the energy are determined by the parameters of the circuit.
To investigate the factors influencing quantum fluctuations,the quantum fluctuations of charge,current and energy in a mesoscopic RLC circuit were calculated in a new Fock space defined by the charge operator using the character of the minimum shift operator based on charge quantization. The results show that,taking account of charge discreteness,the quantum fluctuation of current is zero under the eigenstate of ladder operator,and the fluctuations of charge and energy are determined by charge quantum,Planck constant and state parameters. In addition,the fluctuation of energy depends also on RLC parameters of the circuit,the power source and the external magnetic field.
Starting with the Lagrange of circuit system and using number-phase quantization scheme,mesoscopic LC circuit is quantized and the Hamiltonian expressed by charge number operator and the phase-difference operator is obtained.The quantum fluctuations of both charge number and phase-difference are researched in both vacuum state and squeezed vacuum state.The results show that the quantum fluctuations only relate to the parameters of circuit system in vacuum state,but in the squeezed vacuum state,the quantum fluctuations relate to not only the parameters of circuit system,but also the squeezing parameter.
On the basis of the charge quantization, The quantum fluctuations of the charge, current and energy in the mesoscopic metal ring are calculated by the character of the minimum shift operatorQ∧, the effects of the parameters on the quantum fluctuations are investigated. The results show that, taking account of the charge discreteness, the quantum fluctuations of the charge, energy are not zero under the coherent state, related with the charge quantum and the parameters of the coherent state respectively. In addition, the quantum fluctuations of energy are also determined by the inductance of the mesoscopic metal ring, the external magnetic flux and its time variable rate.
In the inductance-coupling mesoscopic circuit,by taking account of the charge discreteness,a method for calculating quantum effects is proposed in the new Fock space that is formed by the eigenstate of charge operator.In this method,by introducting the minimum shift operator,the system Hamilton and the physics current are expressed according to the charge operator and the ladder operator,and the quantum fluctuations of the charge,current and energy are calculated directly by the character of the ladder operator.The obtained results are related with self-inductance closely.In designing the quantum circuit and the nanoelectroic devices,the considerable factors are given for the quantum noise reduction.
At a definite temperature,a mesoscopic circuit isn't in a determinate quantum state,but in the mixed state.Using the quantum canonic ensemble theory,the quantum fluctuations of charge and circuit of a mesoscopic LC circuit in the mixed state were studied. It is shown that the quantum fluctuations of a mesoscopic LC circuit depend on not only the circuit component parameters,but also the temperature.The higher the temperature,the more quantum noise the mesoscopic LC exhibits.This method is more easily understood and applied than the TFD method.As the mesoscopic circuit is always at finite temperatures,the result is useful for controlling the quantum fluctuations of mesoscopic circuit.