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Journal of Jilin University(Science Edition)

Quasi-classical Description of Mesoscopic Circuit

Yan Liu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

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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.
The quantum double wave theory is applied to the time-dependent mesoscopic LC electric circuit with time-dependent capacitance and inductance. The averages and quantum fluctuations of the electric charge and magnetic flux (electric current) are given for a single time-dependent LC electric circuit. The obtained averages of the electric charge and magnetic flux satisfy the classical equation of motion. After making statistical average over the initial phases, the average and quantum fluctuation of every quantity reduce to that derived by the standard quantum mechanics. These results show that the double wave theory can be used to describe a single time-dependent mesoscopic electric circuit.
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.
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.