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Jiangxi kexue

Time Dependent the Average of the Charge and Current ina Mesoscopic LC Circuit

Yinghua Ji

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The exact wave function of a mesoscopic LC circuit with an external source is obtained using the method of path integrals. We depict and calculate the mean value of the charge and current of the mesoscopic circuit using the two-wave function. The results indicate that one carry out the ensemble mean the two-wave interpretation returns to the usual single wave interpretation.

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The exact wave function of a mesoscopic LC circuit with an external source is obtained using the method of path integrals. We depict and calculate the mean value of the charge and current of the mesoscopic circuit using the two-wave function. The results indicate that one carry out the ensemble mean the two-wave interpretation returns to the usual single wave interpretation.
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.
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 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.