Research PapersNo Access

THE QUANTIZATION OF A MESOSCOPIC TRANSMISSION LINE WITH THE DISCRETENESS OF ELECTRIC CHARGE

YING-HUA JI

Department of Physics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

Key Laboratory of Optoelectronic & Telecommunication of Jiangxi, Nanchang, Jiangxi 330022, China

https://doi.org/10.1142/S0217979209052509Cited by:1 (Source: Crossref)

Abstract

The quantization of a mesoscopic transmission line in accordance with the discreteness of electric charges is proposed under the Born–Von-Karmann periodic boundary condition. The finite-difference Schrödinger equation of the circuit has been obtained in charge representation, and the Schrödinger equation is transformed into Mathieu equation in current representation. The wavefunction and energy spectrum can be solved by adopting the canonical transformation and unitary transformation method. Our results indicate that in the transmission line, quantum fluctuation of currents, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.

Keywords:

PACS: 73.23.-b, 73.23.HK, 03.65.Ca

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