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

Abstract

For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q = en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.

Number-phase quantization of a mesoscopic RLC circuit

“…After that, much work had been done on the complicated electric circuit quantization. [3−10] Instead of the coordinate-momentum quantum variable, [1] references [11]- [13] adopted a numberphase quantization scheme to construct the Hamiltonian operator for an LC circuit and two LC circuits with mutual-inductance, where electric charge takes discrete values. In this paper, we are motivated to adopt this new quantization scheme to further study the RLC circuit.…”