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International Journal of Theoretical Physics

Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature

Shuai Wang

Published Dec 15, 2008• 1 citation
Publisher
DOI
10.1007/s10773-008-9917-5

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Traditionally, the quantization scheme for a mesoscopic LC circuit lies in that electric charge q and electric current L×I are respectively quantized as the coordinate operator Q and momentum operator P. A new quantization scheme is proposed in which number n of the electric charge q(q=en) is quantized as the charge number operator and the relation between electric current and phase operatorθcan be derived, in this way the quantization of mesoscopic LC circuit in the context of number-phase is realized and the corresponding Hamiltonian is obtained. The results show that the Cooper pair number-phase-difference quantization scheme is also available for Josephson junction after introducing the entangled state representation.
For a mesoscopic L-C circuit, besides the Louisell's quantization scheme in which electric charge q and electric current I are respectively quantized as the coordinate operator Q and momentum operator P , in this paper we propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.