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Journal of Jilin University(Science Edition)

Quasi-classical Solutions of Mesoscopic Charge Quantization of LC Circuit

Wei He

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Based on the mean value of a mechanical quantity being a measurable value in experiment and the definition of coherent state,we discussed the charge mean value of the LC circuit and the time evolution formula of the current intensity,the wave function of coherent state and the quasi-classical wave function satisfying the Schrdinger equation.The results show the quasi-classical solution of mesoscopic circuit of charge quantization.

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Based on the mean value of a mechanical quantity being a measurable value in experiment and the definition of coherent state,we discussed the charge mean value of the LC circuit and the time evolution formula of the current intensity,the wave function of coherent state and the quasi-classical wave function satisfying the Schrdinger equation.The results show the quasi-classical solution of mesoscopic circuit of charge quantization.
The authors took the LC circuit as an example to discuss the relationship between the time evolution formula for the charge mean value in mesoscopic circuit and the Kirchoffs law,put forward the equation satisfying the wave function of coherent state,the wave function of coherent state of LC circuit and the quasi-classical wave function satisfying the Schrdinger equation,the current intensity,the quantum fluctuation and the quantum phase,and discussed the motion characteristics of wave packet.
Based on the fundamental fact that the electric charge takes discrete value,the finite-differenced Schrdinger equation of the mesoscopic LC circuit with a source is achieved.With a unitary transformation,the Schrdinger equation becomes the standard Mathieu equation.Using the WKBJ method,the energy spectrum and the wave functions of the system are obtained,the average of currents and square of the current are calculated,the results show the existence of the current fluctuation,which cause the noise in the circuits.
The exact solution of time evolution operator is obtained by applying the gauge transform of algebra dynamic.Such an operator describes the quantum state of time depen- dence of mesoscopic LC circuit containing voltage source.The coherence of quantum state of mesoscopic LC circuit is taken into account.The result showed that the probability of charge stored in capacitor is a motional Gauss wave-packet.The relation between centre charge of wave-packet and voltage source is given.The special example in which the circuit is driven by single rectangle pulse is investigated.