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。     

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.     

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。     

Quantum Systems Connected by a Time-Dependent Canonical Transformation

We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.     

Quantum Systems Connected by a Time-Dependent Canonical Transformation

We study both classical and quantum relation between two Hamiltoniansystems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other istime-dependent Hamiltonian system. The quantum unitary operatorrelevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.     

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.     

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.     

关于有源RLC电路的量子化

提出一种将有源ＲＬＣ电路量子化的方法,修正了有关文献中的错误。     

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     

两网孔介观RLC耦合电路的量子化

从介观电路中经典运动方程出发,运用正则变换的方法对两网孔介观RLC耦合电路的量子化问题进行研究,结果表明其哈密顿量等价于两个独立的谐振子的哈密顿量之和.     

耗散介观电容耦合电路的量子化

通过正则化变换，研究了耗散介观电容耦合电路的量子化，并讨论了系统中电荷和广义电流 的量子涨落. 关键词： 耗散介观电容耦合电路 量子化 正则化变换     

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.     

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.     

Number-phase quantization of a mesoscopic RLC circuit

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.     

Probabilistic Teleportation of an Arbitrary Two-Particle State and Its Quantum Circuits

Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice's Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.     

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.     

交流源作用下介观RLC电路系统量子态随时间的演化

根据量子不变量理论，同时考虑介观电容器极板间电子波函数的耦合作用和电路的耗散,研究介观RLC电路系统在交流电流源作用下动力学的演化过程，并且得到描述系统量子态随时间的演化算符.进一步的分析结果表明，介观RLC电路系统的波函数将由任意的初态演化到一般的压缩态. 关键词： 介观RLC电路 交变电源 不变量理论 时间演化算符     

Evolution of Quantum State for Mesoscopic Circuits with Dissipation

Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that 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.     

Evolution of Quantum State for Mesoscopic Circuits with Dissipation

Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that 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.