Dynamical behavior of a mesoscopic circuit in phonons bath derived by virtue of the IWOP technique

Taking into account the interactions between electrons and phonons, we study the dynamic behavior of a dissipative mesoscopic circuit for pure initial coherent state of phonon bath modes by virtue of the IWOP technique. It shows that if the bath modes are initially in coherent states, some phenomena like Brownian behavior will appear in mean charge and current of the mesoscopic circuit. The quantum fluctuations of charge and current are constant and irrelevant to the coupled coefficients between electrons and phonons.     

Coulomb Blockade of a Mesoscopic RLC Circuit

The quantum theory of the mesoscopic RLC circuit and the condition for Coulomb blockade are given by using canonical quantization and a unitary transformation from the classical equation of motion. Our results show that there is a threshold voltage _T in the circuit. The threshold voltage is related not only to the junction capacitance and inductance, but also to the resistance of the circuit. Generally speaking, the larger the resistance, the larger the threshold voltage. This clarifies the phenomenon of the Coulomb blockade of the dissipative mesoscopic circuit.     

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.     

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.     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明: 有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的; 有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

声子库的量子态对介观电路量子特性影响的研究

考虑电子与声子间相互作用,研究了两种声子库纯初始态(正则系综与粒子数态)下耗散介观电路的动力学特性.长时间极限下(t→∞)：当环境处于热平衡态时,电路系统中的电流和电荷的平均值只与电路所处初始量子态中的平均值有关,与环境无关;环境初态为粒子数态时,电荷与电流平均值随时间的演化特性与环境初始处于热平衡态下时完全一样,表明介观电路中的电荷与电流的平均值与环境量子态的某组占有数无关.电路中电流和电荷的量子涨落不仅与系统的初态有关,还与系统所处环境的量子态及温度有关.一般地说,电路系统与环境的纠缠会 关键词： 介观耗散电路 声子库 量子初态 量子态纯度     

用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明:有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的;有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.     

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.     

无耗散介观电感耦合电路的量子效应

本文从无耗散的电感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其任意的本征态下和压缩真空态下电路中电荷、电流的量子涨落,其结果表明,每个回路中的电荷、电流都存在着量子涨落,且两回路中的量子噪音是相互关联的。     

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.     

介观二阶并联电路的量子涨落

从有源RLC并联电路的经典运动方程出发,通过引入复正则变量,提出了RLC并联电路的量子化方案.作为应用,研究了压缩真空态下介观并联RLC电路中电压,电流的量子涨落,并对结果进行了讨论.     

Quantization,coherent states and geometric phases of a generalized nonstationary mesoscopic RLC circuit

We present an alternative quantum treatment for a generalized mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Taking advantage of the Lewis and Riesenfeld quantum invariant method and using quadratic invariants we obtain exact nonstationary Schrödinger states for this electromagnetic oscillation system. Afterwards, we construct coherent and squeezed states for the quantized RLC circuit and employ them to investigate some of the system’s quantum properties, such as quantum fluctuations of the charge and the magnetic flux and the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary mesoscopic circuit. Finally we evaluate the dynamical and Berry phases for three special circuits. Surprisingly, we find identical expressions for the dynamical phase and the same formulae for the Berry’s phase.     

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.     

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.     

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.     

Mesoscopic photon heat transistor

We show that the heat transport between two bodies, mediated by electromagnetic fluctuations, can be controlled with an intermediate quantum circuit--leading to the device concept of a mesoscopic photon heat transistor (MPHT). Our theoretical analysis is based on a novel Meir-Wingreen-Landauer-type of conductance formula, which gives the photonic heat current through an arbitrary circuit element coupled to two dissipative reservoirs at finite temperatures. As an illustration we present an exact solution for the case when the intermediate circuit can be described as an electromagnetic resonator. We discuss in detail how the MPHT can be implemented experimentally in terms of a flux-controlled SQUID circuit.     

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.     

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.     

Dynamics of a Fermi system with resonant dissipation and dynamical detailed balance

The dissipative dynamics of a system of Fermions is described in the framework of a resonance model—the quantum master equation describes two-body correlations of the system with the environment particles. This equation, with microscopic coefficients depending on the exactly known two-body potential between the system and the environment particles, is discussed in comparison with other master equations, obtained on axiomatic grounds, or derived from a coupling with an environment of harmonic oscillators without altering the quantum conditions. The asymptotic solution is in accordance with the detailed balance principle, and with other generally accepted conditions satisfied during the whole time-evolution: Pauli master equations for the diagonal elements of the density matrix, and damped Bloch–Feynman equations for the non-diagonal ones, that we call dynamical detailed balance. For a harmonic oscillator coupled with the electromagnetic field through dipole interaction, a master equation with transition operators between successive levels is obtained. As an application, the decay width of a quantum logic gate is calculated.