利用热纠缠态表象获得Caldeira-Leggett密度算符方程的积分形式解

开放量子系统,即系统-热库模型,可以用一个关于密度算符的主方程来描述,比如,用来描述固态物理中耗散现象的Caldeira.Leggett主方程.虽然已经有人为了求解此主方程的约化密度矩阵的精确表达式而做过一些努力,但迄今还未见有解答.本文使用了一种全新的方法来求解Caldeira-Leggett方程,用这个新方法可以得到积分形式的显式表达.该方法的要点在于利用有序算符内积分技术把关于密度算符的微分方程首先转化成关于密度态矢量的微分方程,再将密度态矢量投影到热纠缠态表象中,Caldeira-Leggett方程就转变成了关于波函数的微分方程,而波函数是函数.这样就可以使用数学中求解微分方程的方法来求解出波函数.再次利用有序算符内积分技术,再将波函数转化为态矢量和算符,就得到了Caldeira-Leggett方程的积分形势解.     

简并双光子激光的光子统计

从原子和场模的密度算符的主方程出发,应用Haake和Lewenstein所发展的原子变量绝热消除的算符方法,导出了简并双光子激光光场Wigner函数的福克-普朗克(Fokker-Planck)方程及其稳态解.利用稳态解的高斯近似,求得了在不同泵浦强度下,光子统计的解析结果如数值结果,并与前人的结果作了比较.     

自旋为1的粒子的波动方程

对于把克莱因-戈尔登方程当作是玻色子的波动方程的看法提出了异议.给出了一个自旋为1的粒子的相对论性波动方程,该方程具有8×8矩阵或三级四元数的形式,对时间和空间都是一阶导数的;还给出了该种粒子的一些重要算符.在自由粒子的情况下给出了粒子的平面波解和球面波解.     

耗散Jaynes-Cummings模型中微观与唯象学主方程方法的比较

在有耗散的Jaynes-Cummings模型中,对原子与腔复合系统初始处于贝尔态或是原子激发态而腔场为真空态时分别运用微观与唯象学主方程进行求解,并分析这两类主方程在不同耦合区域的区别.结果显示,在强耦合和大失谐情况下,微观主方程求解得到的原子基态的布居数呈线性增长,但唯象学主方程获得的结果却呈非线性增加.在弱耦合区域,这两类主方程求解得到的原子基态布居数都出现快速增加,但是用唯象学主方程要比用微观主方程得到的布居数增加得更快.通过分析与讨论,该结果可能对耗散的腔QED中更好的实现逻辑门提供理论参考.     

原子-辐射场相互作用系统 Heisenberg运动方程的相干态表述

用Heisenberg-Weyle(简称H-W)群直积SU(2)群上的相干态表述了原 子-辐射场相互作用系统的Heisenberg运动方程。引入一个算符振幅函数,将Heisenberg绘 景中算符运动方程转化成可分离变量的偏微分方程,给出了方程的形式解以及时间演化算符 在该表述下的表示。     

Ernst方程的主手征形式与自对偶Yang-Mills场方程

指出Ernst方程可以化为主手征形式, 讨论了轴对称自对偶杨-Mills场(SDYM)与Ernst方程以及主手征形式的关系. 并对H-变换在Ernst方程中的对应作了讨论.     

量子扩散通道中Wigner算符的演化规律

众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况.     

用算符因式分解法解氢原子的径向函数

在初等量子力学的教学中,首先遇到的是求解一维线性谐振子和氢原子等基本问题,通常总是利用级数方法来解此二阶微分算符的本征方程,但往往由于数学上的原因,而使教与学二方面都遇到一定的困难.为此,若将二次量子化中运用的占有数表象及其基本算符(产生算符和湮灭算符)的概念引入后,则上述诸问题均能很简洁地求得所需的本征值和本征函数. 在占有数表象中,任何一个力学量的算符,均可用其二个基本算符来表示,将此原理应用到解具体的薛定谔方程中去时,则原来是一个二阶微分算符的本征方程,可以分解成二个相互伴随的一阶微分算符乘积的本征方程,…     

研究碱金属原子的一个较理想的势能函数

本文对碱金属原子引入势能函数Ｖｒ）＝后解薛定谔方程求得其能量表式，解释了碱金属原子光谱的实验规律．在此基础上，将经典相对论的质量修正相应引入碱金属原子的哈密顿算符中，用近似方法求出其能量的相对论修正的一级近似．这是用量子力学方法讨论碱金属原子的一种简略方法，也是一种粗略的近似．     

耗散Jaynes-Cummings模型中微观与唯象学主方程方法的比较

在有耗散的Jaynes-Cummings模型中,对原子与腔复合系统初始处于贝尔态或是原子激发态而腔场为真空态时分别运用微观与唯象学主方程进行求解,并分析这两类主方程在不同耦合区域的区别．结果显示,在强耦合和大失谐情况下,微观主方程求解得到的原子基态的布居数呈线性增长,但唯象学主方程获得的结果却呈非线性增加．在弱耦合区域,这两类主方程求解得到的原子基态布居数都出现快速增加,但是用唯象学主方程要比用微观主方程得到的布居数增加得更快．通过分析与讨论,该结果可能对耗散的腔QED中更好的实现逻辑门提供理论参考．     

Ket-Bra纠缠态方法研究含时外场中与热库耦合Qubit的演化

采用Ket-Bra纠缠态方法求解主方程, 研究了具有含时外场情况下单qubit和无相互作用的两qubit与热库耦合时的量子退相干、退纠缠现象. 对两qubit情形, 我们以共生纠缠度(concurrence)作为纠缠度量, 研究了其纠缠动力学演化过程. 研究表明即使系统内部不存在直接、间接的相互作用, 施加含时外场也能引起纠缠的震荡和复活, 这为通过施加控制外场抑制开放系统的退相干、退纠缠过程提供了理论支持.     

Decoherence of Two-qubits Coupled with Reservoirs Studied with New Ket-Bra Entangled State Method

For the first time we define a so-called Ket-Bra Entangled State (KBES) for two-qubits coupled with reservoirs by introduce an extra fictitious mode vector, and convert the corresponding master equation into Schrödinger-like equation by virtue of this state. Via this approach we concisely obtain the dynamic evolution of two uncoupled qubits each immersed in local thermal noise. Based on this, the decoherence evolution for the extended Werner-like states is derived and how purity and temperature influence the concurrence is analyzed. This KBES method may also be applied to tackling master equations of limited atomic level systems.     

Two-Soliton Bound States in a Heisenherg Spin Chain

An inhomogeneous Heisenberg spin Hamiltonian with single ion anisotropy is used to investigate the nonlinear excitations in ferromagnetic chain. By means of the Holstein-Primakoff transformation and Glauber's coherent-state representation, the equation of motion for anni-hilation operator a(j) is reduced to a nonlinear Schrödinger-like equation in the semiclassical approximation and the long wave approximation. For a homogeneous system, the exact and explicitly single soliton (localized magnon state) and two-magnon bound state solutions are Given by the inverse scattering transform.     

Influence of Lamb Shift Parameter on Dissipative Dynamics of the Phase Damped Jaynes–Cummings Model with Gravity Under Markovian Approximation

In this paper, we study the dissipative dynamics of the phase damped Jaynes–Cummings model with gravity under Markovian approximation in the presence of the Lamb shift parameter. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a phase damping mechanism. We first present the master equation for the reduced density operator of the system under Markovian approximation in terms of a Hamiltonian describing the atom-field interaction with gravity in the presence of Lamb-shift parameter. Then, by making use of the super-operator technique, we obtain an exact solution of the master equation. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, we investigate the influence of Lamb shift parameter on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing and atomic momentum diffusion in the presence of phase damping.     

The master equation for a two-level atom in a laser field with squeezing-like terms

In this paper, we derive the time dependent solution of the effective master equation for the reduced density matrix operator of a two-level atom driven by a strong classical field and damped into a “modelled” reservoir with non-flat density of modes. The effects of different parameters on the atomic inversion, the von Neumann entropy and the entropy squeezing are discussed.     

Quantum Master Equation with Damping Operator Including Interaction Effect for the Raman-Coupled Model with Cavity Damping

The irreversible time-evolution of the Raman-coupled model which is placed in a lossy cavity is investigated by means of the quantum master equation together with the Lie algebra method. Unlike the previous works, the effect of the interaction between the two-level atom and cavity photon on the damping operator of the quantum master equation is taken into account. To examine how the interaction effect influences the time-evolution of the relevant system, the atomic inversion and the Husimi Q-function of the cavity photon are calculated.     

Influence of a Classical Homogeneous Gravitational Field on Dissipative Dynamics of the Phase Damped Jaynes–Cummings Model under the Markovian Approximation

In this paper, we study the dissipative dynamics of the phase damped Jaynes–Cummings model under the Markovian approximation in the presence of a classical homogeneous gravitational field. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a phase damping mechanism. We first present the master equation for the reduced density operator of the system under the Markovian approximation in terms of a Hamiltonian describing the atom-field interaction in the presence of a homogeneous gravitational field. Then, by making use of the super-operator technique, we obtain an exact solution of the master equation. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, we investigate the influence of gravity on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field in the presence of phase damping.     

Exact Solution for Non-Markovian Master Equation Using Hyper-operator Approach

Non-Markovian master equation of Harmonic oscillator and two-level systems are investigated using the hyper-operator approach. Exact solution of time evolution operator of Harmonic oscillator is obtained exactly. For two-level system the time evolution operator is exactly found and coefficients satisfy ordinary differential equation.     

Damping-like effects in Heisenberg spin chain caused by the site-dependent bilinear interaction

We investigate a continuous Heisenberg spin chain equation which models the local magnetization in ferromagnet with time-and site-dependent inhomogeneous bilinear interaction and timedependent spin-transfer torque.By establishing the gauge equivalence between the spin chain equation and an integrable generalized nonlinear Schr?dinger equation,we present explicitly a novel nonautonomous magnetic soliton solution for the spin chain equation.The results display how the dynamics of the magnetic soliton can be controlled by the bilinear interaction and spin-polarized current.Especially,we find that the site-dependent bilinear interaction may break some conserved quantity,and give rise to damping-like effect in the spin evolution.     

Radiation reaction

I solve Maxwell's equation for a current produced by a classical, point electron. My solution, which represents the self electromagnetic field of the electron, can be found along the electron trajectory, where the conventional retarded-time solution is singular. The solution is in the form of an integral over all spectral frequencies of the field and has an Ehrenfest correspondence with the operator field of quantum electrodynamics (QED). Use of the field in the equation of motion for a harmonically-bound electron leads to an equation having the same form as the Schrödinger equation for a two-level atom interacting with the QED vacuum field.