Macroscopic Quantum Coherent Phenomena in the Mesoscopic Electric Circuit

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with external source which is the time function has been proposed. By using the instanton methods, the macroscopic quantum coherent phenomena and effective capacitance oscillation in the mesoscopic electric circuit have been addressed.     

Bloch wave oscillation and Coulomb blockade in mesoscopic electric circuits

The quantum theory for mesoscopic electric circuits with charge discreteness is briefly described. The Schrödinger equation of the mesoscopic electric circuit with an external source which is the time function has been proposed. The Bloch wave oscillation and Coulomb blockade in the mesoscopic electric circuit have been addressed.     

Effect of scattering in the mesoscopic pure L design electric circuit

The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The effect of scattering in mesoscopic ‘pure’ inductance design circuit, just like in the mesoscopic metallic rings has been address. The quantum characteristics of charge diffusion has also been obtained explicitly. The case in finite temperature has been discussed as well.     

电荷不连续时电容耦合介观电路的量子回路方程及其能谱

考虑电荷具有不连续性的事实对双LC介观电路进行量子化,给出耦合形式的量子回路方程以及无相互作用Hamilton本征基矢下的电路能谱.结果表明,计及电荷离散性将使回路方程的形式发生明显变化;介观电路的能谱除与电路参数相关外,还明显地依赖于电荷的量子化性质.     

介观RLC电路的量子效应

将介观电容器看作介观隧道结,对介观RLC电路作了相应的量子力学处理.研究了介观RLC电路系统的量子态演化.研究表明:考虑介观电容耦合效应的影响,介观RLC电路系统将由初始的Fock态演化到压缩Fock态,并讨论了电荷及磁通在压缩Fock态下的量子涨落.     

有源介观LC电路的量子涨落

本文利用含时微扰论,研究了电源幅值较小时介观LC电路中电荷与电流的量子涨落。在确定的温度下,系统将处在混合态,进一步得到有限温度下含源介观LC电路的量子涨落。研究表明有源介观LC电路的量子涨落不仅与电路参数有关,还与时间和温度有关。     

Asymmetric Double Quantum Dots as a Subminiature Mesoscopic Cell

A subminiature mesoscopic cell,consisting of asymmetric double quantum dots capacitively coupled to a nearby mesoscopic circuit,is proposed,which can transform disordered noise energy to ordered electric energy.Two schemes,the noises originating from the nearby mesoscopic circuit and from the electromagnetic wave disturbance in external environment,are investigated.We found that the proposed cell can manifest as a good constant current source and the output current may not reach its largest value even if the circuit is shorted.     

Quantum Effect in a Diode Included Nonlinear Inductance-Capacitance Mesoscopic Circuit

The mesoscopic nonlinearinductance-capacitance circuit is a typical anharmonicoscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoscopic circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schrödinger equation of the system is a four-order difference equation in \hat{p} representation.Using the extended perturbative method, the detail energy spectrumand wave functions are obtained and verified, as an application ofthe results, the current quantum fluctuation in the ground state iscalculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopic circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.     

Quantum Effects of Mesoscopic Inductance and Capacity Coupling Circuits

Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finite-difference Schrödinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrödinger equation can be divided into two Mathieu equations in \hat p representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.     

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

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.     

The Quantization of Mesoscopic Electric Circuit with the Discreteness of Electron Charge

The importance of discreteness of electron charge for mesoscopic electric circuit is addressed. A quantization bf the circuit in accord with the discreteness of electric charges is proposed, and a Schrödinger equation incharge representation'is obtained. The Schrödinger equation is turned to be Mathieu equation in'current representation', the wavefunction and energy spectrum can be solved exactly. The WKB solutions of the energy levels for the ground state and the excited states are given.     

介观电路中电荷的量子效应

基于介观电路中电荷是量子化的基本事实，给出了介观电路的量子理论，并讨论了介观ＬＣ电路的量子涨落 关键词：     

Quantum Effect in the Mesoscopic RLC Circuits with a Source

The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of.the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of currents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.     

Quantum Effect in the Mesoscopic RLC Circuits with a Source

The research work on the quantum effects in mesoscopic circuits has undergone a rapid development recently, however the whole quantum theory of the mesoscopic circuits should consider the discreteness of the electric charge. In this paper, based on the fundamental fact that the electric charge takes discrete values, the finite-difference Schrodinger equation of the mesoscopic RLC circuit with a source is achieved. With a unitary transformation, the Schrodinger equation becomes the standard Mathieu equation, then the energy spectrum and the wave functions of the system are obtained. Using the WKBJ method, the average of durrents and square of the current are calculated. The results show the existence of the current fluctuation, which causes noise in the circuits. This paper is an application of the whole quantum mesoscopic circuits theory to the fundamental circuits, and the results will shed light on the design of the miniation circuits, especially on the purpose of reducing quantum noise coherent controlling of the mesoscopic quantum states.     

Radiating frequency of three-loop mesoscopic LC circuit with mutual inductance obtained by IEO method

Instead of normally tackling electric circuits by virtue of the Kirchhoff's theorem whose aim is to derive voltage,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(IEO) method to realize our aim.     

Number-Phase Quantization Scheme for L-C Circuit

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.     

感性神经元模型及其动力学特性研究

神经元的大小属于介观尺度范围,本文考虑神经元的电感特性,建立了由细胞膜电感、膜电容、钾离子忆阻器和氯离子电阻构成的神经元经典电路模型和介观电路模型.利用经典电路理论和介观电路的量子理论,推导了在外部冲击激励下神经元细胞膜电压响应的表达式.将枪乌贼神经元的电生理参数代入膜电压表达式并计算可知,两种模型下的膜电压均先增大后减小,最后达到零值的静息状态,且其能量主要集中在0—30 Hz的脑电频率范围内.进一步比较发现,介观电路模型下膜电压的峰值及达到峰值所需的时间(达峰时间)均低于经典电路模型下的值,并与枪乌贼轴突受到刺激后的实验结果更接近,说明介观电路模型更能反应神经元受到刺激后的生理特征.基于介观电路模型,随着外部激励强度的增加,膜电压的峰值增加且达峰时间变短.膜电压峰值及达峰时间等参数更易受神经元膜电容的影响.神经元的介观电路模型对于理解神经元受到刺激后的兴奋性,推动受大脑功能启发的量子神经网络的发展等具有重要意义.     

感性神经元模型及其动力学特性研究

神经元的大小属于介观尺度范围,本文考虑神经元的电感特性,建立了由细胞膜电感、膜电容、钾离子忆阻器和氯离子电阻构成的神经元经典电路模型和介观电路模型.利用经典电路理论和介观电路的量子理论,推导了在外部冲击激励下神经元细胞膜电压响应的表达式.将枪乌贼神经元的电生理参数代入膜电压表达式并计算可知,两种模型下的膜电压均先增大后减小,最后达到零值的静息状态,且其能量主要集中在0—30 Hz的脑电频率范围内.进一步比较发现,介观电路模型下膜电压的峰值及达到峰值所需的时间(达峰时间)均低于经典电路模型下的值,并与枪乌贼轴突受到刺激后的实验结果更接近,说明介观电路模型更能反应神经元受到刺激后的生理特征.基于介观电路模型,随着外部激励强度的增加,膜电压的峰值增加且达峰时间变短.膜电压峰值及达峰时间等参数更易受神经元膜电容的影响.神经元的介观电路模型对于理解神经元受到刺激后的兴奋性,推动受大脑功能启发的量子神经网络的发展等具有重要意义.     

磁场对介观耦合金属环中持续电流的影响

在考虑电荷是量子化的基础上，研究了外加磁场对介观耦合金属环中持续电流的影响.结果表明：由于存在耦合，介观金属环中总是存在附加的持续电流，附加的持续电流与电路参数及耦合系数有关.当外加磁通量按正弦规律变化时，介观耦合金属环中出现倍频与分频效应. 关键词： 介观耦合金属环 持续电流 磁场     

Research on Quantum Effects of Coupled Double Resonance Circuit Using the Scheme of Gauss Propagator

The time evolvement of quantum state has been researched by the schemes of Louisell’s common canonical quantization and Gauss Propagator for mesoscopic coupled double resonance circuit with electrical sources. Moreover, the formulae of time evolvement wave function and transition probability of quantum state of this circuit are given. It is more significant for the quantitative analysis quantum character of mesoscopic circuit.