有源介观RLC电路的量子涨落

通过正则变换将有源介观RLC电路进行了量子化,运用路径积分方法求出了介观RLC电路的波函数.由该波函数严格计算了电荷、电流的量子涨落.     

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：     

低温下介观电路的量子涨落

从有源RLC回路的运动方程出发,用涨落一耗散定理,研究了回路的能量涨落,电荷及电流涨落,发现低温下这些涨落是属量子力学效应,并给出了电荷、电流的测不准关系;而在温度升高时,涨落是经典的热力学涨落,量子力学效应被淹没. 关键词：     

压缩真空态下介观电路的量子涨落

从有源LC回路的运动方程出发，研究了在压缩真空态下介观LC电路中电荷、电流的量子涨落． 关键词：     

介观二阶电路量子涨落的对偶性

讨论了阻尼对介观耗散电路中电荷和电流量子涨落的影响，在能量本征态下比较了介观RLC串、并联电路中电荷和电流的量子涨落，发现它们之间具有对偶性。     

介观电容耦合电路的量子涨落

从无耗散的电容耦合电路的经典运动方程出发，分别研究了这一耦合电路在任一本征态下和在压缩真空态下电荷、电流的量子涨落.结果表明，两个回路中的量子噪声是相互关联的. 关键词：     

有源轻阻尼RLC介观电路中的波函数及电荷、电流的量子涨落

从有源RLC电路运动方程出发,通过量子化有源RLC电路,计算了低温下电流、电荷的量子涨落以及电源对量子涨落的影响.     

介观电容耦合LC电路在有限温度下的能量及热效应

由正则量子化方法导出了介观电容耦合LC电路体系的哈密顿算符, 利用幺正变换使哈密顿算符对角化. 用系综理论给出了体系的平均能量及其涨落, 在此基础上, 借助于广义Hellmann-Feynman定理, 讨论了有限温度下电路体系中电荷与自感磁通的量子涨落. 结果表明, 体系中电荷与自感磁通的量子涨落不仅与电路元件参数有关, 而且还与温度有关.     

介观串并联RLC电路的量子涨落

借鉴阻尼谐振子的量子力学处理的研究思想,将介观RLC串并联电路量子化．在此基础上,研究了真空态下各支路电流和电压的量子涨落．结果表明,各支路电流电压的量子涨落均与电路器件的参数有关,且随时间衰减．     

有源RLC介观电路的量子涨落

使用正则交换和幺正变换的方法，研究了有源RLC介观电路的量子涨落。结果表明电源电动势ε(t)的有无对电荷和电流的量子涨落没有影响。     

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.     

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.     

Marginal Distributions of Wigner Function in a Mesoscopic L-C Circuit at Finite Temperature and Thermal Wigner Operator

Wigner function in phase space has its physical meaning as marginal probability distribution in coordinate space and momentum space respectively, here we endow the Wigner function with a new physical meaning, i.e., its marginal distributions’ statistical average for q ²/(2C) and p ²/(2L) are the energy stored in capacity and in inductance of a mesoscopic L-C circuit at finite temperature, respectively. PACS numbers: 03.65.-w, 73.21.-b     

Quantum Fluctuation of a Mesoscopic Inductance Coupling Circuit at Finite Temperature

We study the quantization of mesoscopic inductance coupling circuit and discuss its time evolution. Bymeans of the thermal field dynamics theory we study the quantum fluctuation of the system at finite temperature.     

介观互感耦合阻尼并联双谐振电路的量子涨落

对介观互感耦合阻尼并联电路作双模耦合阻尼谐振子处理,将其量子化.通过三次幺正变换,将体系的哈密顿量对角化.在此基础上给出了体系的本征能谱,研究了Fock态、真空态下各回路电流和电压的量子涨落.     

有互感和电源的介观耦合电路的量子涨落

通过正则变换和幺正变换的方法研究了有互感和电源存在的情况下的介观电容耦合电路的量子涨落.结果表明电荷和电流的量子涨落与电源无关;互感的有无对涨落的影响很大;适当选取回路中电器件的参数,可以控制耦合系数K对涨落的影响.并且,每个回路中电荷和电流的量子涨落是相互制约的.     

Invariants and Quantum Fluctuations of a Mesoscopic RLC Circuit in a Squeezed State and Squeezed Number State

The invariants for a mesoscopic RLC circuit with a power source are studied and used to construct the squeezed states and squeezed number states for the system. The quantum fluctuations of the mesoscopic RLC circuit in the squeezed states and squeezed number states are also investigated.     

The Quantum Fluctuations of Mesoscopic Damped Mutual Capacitance Coupled Double Resonance RLC Circuit in Excitation State of the Squeezed Vacuum State

Mesoscopic damped double resonance mutual capacitance coupled RLC circuit is quantized by the method of damped harmonic oscillator quantization. The Hamiltonian is diagonalized by unitary transformation. The eigenenergy spectra of this circuit are given. The quantum fluctuations of the charges and current of each loop are researched in excitation state of the squeezed vacuum state, the squeezed vacuum state and in vacuum state. It is show that, the quantum fluctuations of the charges and current are related to not only circuit inherent parameter and coupled magnitude, but also quantum number of excitation, squeezed coefficients, squeezed angle and damped resistance. And, because of damped resistance, the quantum fluctuation decay along with time. PACS numbers: 03.65.-w,42.50.Lc.     

The Squeezing Effect in a Mesoscopic RLC Circuit

Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely,the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit.If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also findthat uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.     

Josephson-Like Effects in the Mesoscopic Electric Circuit

Abstract The quantum theory for mesoscopic electric circuit with charge discreteness is briefly described. The Schrodinger equation of the mesoscopic electric circuit with external source which is a time function has been proposed. The Josephson-like effects in the mesoscopic electric circuit have been addressed.