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.     

Quantum Fluctuation in Thermal Vacuum State for a Mesoscopic RLC Circuit

By means of the thermal field dynamics theory invented by Takahashi and Umezawa, we study the quantum effects of a nondissipative mesoscopic RLC circuit at a finite temperature.     

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.     

介观RLC电路的精确波函数和压缩态

利用一系列幺正变换求出了介观RLC电路的精确波函数和基本不变量,并发现此系统基本不变量的本征态是压缩态,它可用介观RLC电路的精确波函数来构造。     

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.     

Quantum Fluctuations in Thermal Vacuum State for Two LC Circuits with Mutual Inductance

By means of thermal field dynamics theory, we study the quantum fluctuations of two LC circuits with mutual inductance at a finite temperature.     

Quantum fluctuations of mesoscopic damped double resonance RLC circuit with mutual capacitance--inductance coupling in thermal excitation state

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.     

Thermodynamics of Squeezed State for Mesoscopic RLC Circuits

We present a density matrix of a mesoscopic RLC circuits to make it possible to analyze the connection between the initial condition and the certain temperature. Our results show that the quantum state evolution will be closely related to the initial condition; the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially. In addition, we also obtain squeezed minimum uncertainty state with satisfying certain condition in mesoscopic RLC circuit.     

介观并联RLC电路的量子涨落

将介观并联RLC电路量子化，并利用幺正变换给出其波函数及能谱的精确解.在此基础上获得各支路中电流和电压的量子涨落. 关键词： 并联RLC电路 幺正变换 量子涨落     

Quantum Fluctuations of the Current and Voltage in Thermal Vacuum State for Mesoscopic Quartz Piezoelectric Crystal

The mesoscopic quartz piezoelectric crystal equivalent circuit is quantized by the method of damped harmonic oscillator quantization. It is shown that, when each branch is in the thermal vacuum states, the quantum fluctuations of the voltage, and current of each loop relate with not only the equivalent circuit inherent parameter, but also the temperature and decay according to exponent along with time.     

Quantum Effects of Mesoscopic RLC Circuit in Squeezed Vacuum State

Starting from the equation of motion of anactive RLC circuit, the quantum effects of charge andcurrent in the mesoscopic circuit (RLC circuit) in thesqueezed vacuum state are investigated.     

Quantum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

We study the quantum fluctuations of the charge and current of two L-C dissipative mcsoscopic circuit withthe mutual inductance in the vacuum state. Our results show that the system state will evolve to a squerzcd coherentstate under the effect of external source. We find that the squeezing amplitude parameter is relative to the parametersof circuit and the mutual-inductance coefficient in the existence of dissipation. Whcn the circuit has no dissipation orthere is complete coupling between two meshes, the squeezing amplitude parameter only depends on the capacitance'sratio.     

有源RLC介观电路量子化过程中幺正算符的选择

采用正则变换和正变换方法对有源RLC介观电路实现了量子化，通过构造几种不同形式的幺正算，对介观电路实施量子化的计算过程的比较分析，得到了构造幺正算符的最佳方案，该方案能够使正则变换与幺正变换的结果完全吻合。     

Quantum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

We study the quantum fluctuations of the charge and current of two L-C dissipative mesoscopic circuit with the mutual inductance in the vacuum state.Our results show that the system state will evolve to a squeezed coherent state under the effect of external source.We find that the squeezing amplitude parameter is relative to the parameters of circuit and the mutual-inductance coefficient in the existence of dissipation.When the circuit has no dissipation or there is complete coupling between two meshes,the squeezing amplitude parameter only depends on the capacitance‘s ratio.     

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．     

介观RLC电路在热真空态下的量子涨落

利用热场动力学的方法研究了介观RLC电路在具有热噪声的真空态下电荷和磁通(电流)的量子涨落.从而得到了有限温度下这一电路在热真空态下的量子涨落与温度的关系.结果表明,介观RLC电路的量子涨落不仅与电路中的元件参量和电路的共振频率ω有关,而且与温度T有关.温度越高,介观RLC电路的量子噪声越大 关键词： 介观RLC电路 热真空态 量子涨落     

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.     

非线性电容RLC串联电路的主共振研究

研究非线性电容RLC串联电路,应用多尺度法,得到非线性振动系统主共振的一次近似解并进行数值计算,分析电阻、电感、电容和电动势对主共振幅频响应的影响.结果表明:RLC串联电路的主共振响应有跳跃和滞后现象;随着电动势的增加,主共振的振幅和共振区增大;随着电阻的增大,主共振的振幅和共振区减小.