By employing the continuous parameter entangled state representations, we investigate the energy level and the wave function for a capacitively and mutual-inductively coupled LC mesoscopic circuit. It is found that in...By employing the continuous parameter entangled state representations, we investigate the energy level and the wave function for a capacitively and mutual-inductively coupled LC mesoscopic circuit. It is found that investigating the meso- scopic circuit in such representations can bring us the following conveniences. Firstly, the dynamical equation is naturally transformed into a single-variable differential equation. Second/y, the center-of-mass kinetic energy is included in the energy level of the system. Thus it is instructive to introduce the entangled state representation into the investigation of mesoscopic circuits.展开更多
Instead of normally tackling electric circuits by virtue oI the Klrctllaott＇s theorem wnose aim is to uerlvc voxt^gc, electric current, and electric impedence, our aim in this paper is to derive the characteristic fr...Instead of normally tackling electric circuits by virtue oI the Klrctllaott＇s theorem wnose aim is to uerlvc voxt^gc, electric current, and electric impedence, our aim in this paper is to derive the characteristic frequency of a three-loop mesoscopic LC circuit with three mutual inductances, e.g., for the radiating frequency of the three-loop LC oscillator, we adopt the invariant eigen-operator （lEO） method to realize our aim.展开更多
Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics （TFD）, the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is propo...Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics （TFD）, the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.展开更多
With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamilt...With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.展开更多
For a mesoscopic L-C circuit,besides the Louisell's quantization scheme in which electric charge q andelectric current I are respectively quantized as the coordinate operator Q and momentum operator P,in this pape...For a mesoscopic L-C circuit,besides the Louisell's quantization scheme in which electric charge q andelectric current I are respectively quantized as the coordinate operator Q and momentum operator P,in this paperwe propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangianformalism.The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11147009 and 11244005)the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2010AQ027 and ZR2012AM004)
文摘By employing the continuous parameter entangled state representations, we investigate the energy level and the wave function for a capacitively and mutual-inductively coupled LC mesoscopic circuit. It is found that investigating the meso- scopic circuit in such representations can bring us the following conveniences. Firstly, the dynamical equation is naturally transformed into a single-variable differential equation. Second/y, the center-of-mass kinetic energy is included in the energy level of the system. Thus it is instructive to introduce the entangled state representation into the investigation of mesoscopic circuits.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)
文摘Instead of normally tackling electric circuits by virtue oI the Klrctllaott＇s theorem wnose aim is to uerlvc voxt^gc, electric current, and electric impedence, our aim in this paper is to derive the characteristic frequency of a three-loop mesoscopic LC circuit with three mutual inductances, e.g., for the radiating frequency of the three-loop LC oscillator, we adopt the invariant eigen-operator （lEO） method to realize our aim.
基金Project supported by the Natural Science Foundation of Heze University of Shandong Province, China （Grant No XY05WL01）, the University Experimental Technology Foundation of Shandong Province, China （Grant No S04W138）, the Natural Science Foundation of Shandong Province, China （Grant No Y2004A09） and the National Natural Science Foundation of China （Grant No 10574060）.
文摘Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics （TFD）, the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.
文摘With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.
基金The project supported by the President Foundation of the Chinese Academy of Sciences
文摘For a mesoscopic L-C circuit,besides the Louisell's quantization scheme in which electric charge q andelectric current I are respectively quantized as the coordinate operator Q and momentum operator P,in this paperwe propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangianformalism.The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.
