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Journal of Yanbian University

The generalized momentum and kinetic momentum of mesoscopic RLC circuit

Shou Zhang

Published Jan 1, 2003• 0 citations
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Abstract

In this article, we discuss the uncertainty relations in two kinds of circumstances like generalized coordinates, generalized momentum and kinetic coordinates, kinetic momentum of mesoscopic RLC by the method of unitary transformation. The results of the former are acquired of index number relation with time, where as the latter have not any relations as time goes.

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In this article, we discuss the uncertainty relations in two kinds of circumstances like generalized coordinates, generalized momentum and kinetic coordinates, kinetic momentum of mesoscopic RLC by the method of unitary transformation. The results of the former are acquired of index number relation with time, where as the latter have not any relations as time goes.
The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as well as the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.
The mesoscopic RLC series circuit are quantized by five different ways which are the forced damp harmonic vibration,the construct the Hamiltonian and associated canonical transformation,the damped harmonic vibration canonical transformation,the construct the Hamiltonian and associated unitary transformation and the inner construction of the resistance are summarized.The quantum fluctuations of the charge,the current and their products are analyzed when the system in the vacuum state.The different results from the same circuit quantized by different methods are due to the different chice of the Hamiltonion of the system.