耗散子运动方程与福克-普朗克量子主方程（英文）

发展非线性耦合环境下精确、非微扰的量子耗散方法仍然是一个巨大的挑战.本文针对线性和二次耦合热浴模型,介绍了两种刻画系统与环境耦合动力学的有效方法.一个是耗散子运动方程(DEOM)理论,最近己被扩展到处理非线性耦合环境.另一个是推广的福克-普朗克量子主方程(FP-QME)方法,将在这项工作中基于DEOM推导给出.本文对这两种方法进行了详细的比较,并重点介绍了所涉及的准粒子图像、物理含义以及实现方案.     

量子耗散微扰方法的适用性

将微扰量子耗散理论得出的两态线性吸收光谱与严格结果相比较. 所考虑的近似理论为两套完备两阶量子耗散方程,其一为标准的编时微扰方法,另一为所谓的完备二阶驱动耗散耦合方程. 对于两态线性吸收光谱,可以得到解析解,将结果与严格公式比较,来评估这两种方法的适用性和应用范围.     

费米型级联运动方程的绝热截断方案

研究开放量子系统的量子耗散动力学对于理解许多新奇量子现象背后的机制和实现量子器件的精确量子态控制具有重要意义. 级联运动方程方法已成为研究这类量子耗散动力学最常用的数值方法之一. 然而，在处理强电子关联系统时，准确描述强关联效应需要高的级联截断层数. 这导致级联运动方程方法需要耗费大量物理内存和计算时间. 为了解决该问题，将具有最快耗散速率的耗散模式与其他较慢的耗散模式分离，提出了一种级联运动方程的绝热截断方案. 在单杂质安德森模型上进行的数值测试表明，与传统的方案相比，该截断方案显著地降低了级联运动方程收敛需要的截断层数. 此外，该截断方案缓解了长时间耗散动力学中的数值不稳定性.     

耗散系统中压缩态的产生

对于一个用于产生压缩态的典型的耗散系统，我们利用非主方程方法，得到其严格的解析解，这种处理方法为解决许多量子耗散问题提供了一种精确（不作任何近似）而简洁的途径。     

量子纠缠与宇宙学弗里德曼方程

量子纠缠作为量子信息理论中最核心的部分,代表量子态一种内在的特性,是微观物质的一种根本的性质,它是以非定域的形式存在于多子量子系统中的一种神奇的物理现象.熵也是量子信息理论的重要概念之一,纠缠熵作为量子信息的一个测度已经成为一种重要的理论工具,为物理学中的各类课题提供了新的研究方法.本文主要考虑量子纠缠的宇宙学应用,试图更好地从纠缠的角度来理解宇宙动力学.本文研究了量子信息理论的概念和宇宙学之间的深层联系,利用费米正则坐标和共形费米坐标构建了弗里德曼- 勒梅特-罗伯逊-沃尔克宇宙学弗里德曼方程和纠缠之间的联系.假设小测地球（a geodesic ball）的纠缠熵在给定体积下是最大的,可以从量子纠缠第一定律推导出弗里德曼方程.研究表明引力与量子纠缠之间存在着某种深刻的联系,这种联系对引力场方程的解是成立的.     

量子噪音与量子Langevin方程

介绍了量子噪音和量子Langevin方程 ,并与经典噪音和经典Langevin方程进行了比较 .量子噪音来源于两种途径 ,第一种与经典噪音相似 ,第二种则起源于Heisengberg测不准原理 .同时 ,也简略给出了量子Langevin方程的推导.The properties of quantum noise and Langevin equation are discussed. Comparisons between the quantum noise and Langevin eqution and the classic one are presented. A brief derivation for quantum Langevin equation is showed. The quantum noise comes from two ways, namely, the way as same as that of classic noise and the Heisenberg uncertainty.     

原子分子光子系统的耗散相互作用和退相干

原子分子系统与量子化的电磁场或光子模式耦合的系统是非相对论量子力学理论研究和实验研究的主要对象和模型. 现实系统必然与外界环境耦合，且即便原子隔绝较好、光学腔壁品质因子足够高，原子系统也不等价于少数几个能级构成的简单模型：它仍然有不为零的几率跃迁到不可控的能级空间、与原子相互作用的自由空间真空场的量子效应也必须考虑. 本文将结合开放量子系统理论的基本要素与原子光子的基本模型，对原子分子系统在电磁场中发生的耗散以及量子退相干过程做简单综述，并重点介绍描述量子系统退相干过程的主流理论工具——主方程.     

耗散介观电容耦合电路的量子效应

对介观耗散电容耦合电路作阻尼谐振子处理,将其量子化,在此基础上研究电荷和电流在能量本征态下的量子涨落,并对其进行讨论.结果表明,每个回路的电荷、电流都存在量子涨落,且两回路的量子噪声是相互关联的. 关键词： 介观耗散电路 电容耦合 量子涨落     

广义量子主方程：教程综述和最新进展

广义量子主方程(GQME)为模拟嵌入在量子环境中的开放量子体系的约化动力学提供了一种通用且严格的计算方法. 开放量子体系的动力学在能量、电荷以及量子相干转移过程和光化学反应中至关重要. 量子系统通常被定义为我们感兴趣的自由度,例如捕光分子的电子态或凝聚态体系中的特定振动模式. 系统周围的环境也被称为热浴,必须考虑它对系统的影响. 例如,广义量子主方程理论中用投影算符方法对其进行描述. 本综述总结了广义量子主方程的两种标准形式,即时间卷积形式的Nakajima-Zwanzig GQME和无卷积形式的广义量子主方程. 在更流行的NZ-GQME形式中,记忆核刻画了非马尔可夫和非微扰效应,给出了约化密度矩阵的精确量子动力学. 总结了几种通过含有分子信息但无投影算符的时间关联函数作为输入信息,进而求解含投影算符的记忆核的方法. 特别值得一提的是近期提出的NZ-GQME改进版方法,该方法是基于将哈密顿量划分为更通用的对角和非对角部分. 上述系统相关的热浴时间关联函数可以通过数值精确或近似量子动力学方法计算. 本文将有助于理解广义量子主方程的理论背景,并且展望通过GQME与量子计算技术的结合解决使用当今最先进的经典超级计算机无法解决的与量子动力学和量子信息相关的复杂问题.     

单光子量子路由的耗散影响

单光子量子路由对于在芯片中实现量子信息交换具有重大意义。研究单光子量子路由中的耗散影响能够更加真实的模拟实际实验的结果。研究发现耗散能级的存在使得同等条件下的量子路由概率减小,并且需要相对较强的耦合才能取得最大量子路由概率。同时,也建立了共振条件下量子路由概率同耦合强度以及耗散强度间的关系。     

Schrödinger Equation for An Extended Electron

A new quantum mechanical wave equation describing the dynamics of an extended electron is derived via Bohmian mechanics. The solution to this equation is found through a wave packet approach which establishes a direct correlation between a classical variable with a quantum variable describing the dynamics of the center of mass and the width of the electron wave packet. The approach presented in this paper gives a comparatively clearer picture than approaches using elaborative manipulation of infinite series of operators. It is shown that the new Schrödinger equation is free of any runaway solutions or any acausal responses.     

Exact Solutions to the Quantum Rabi-Stark Model Within Tunable Coherent States

The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling is present on an equal footing, is studied within the tunable extended coherent states. The eigenvalues and eigenstates are therefore obtained exactly. Surprisingly, the entanglement entropy in the ground-state is found to jump suddenly with the coupling strength. The first-order quantum phase transition can be detected by level crossing of the ground state and the first excited state, which is however lacking in the original linear quantum Rabi model. Performing the first-order approximation in the present theory, we can derive closed-form analytical results for the ground-state. Interestingly, it agrees well with the exact solutions up to the ultra-strong coupling regime in a wide range of model parameters. The spectral collapses when the absolute value of the nonlinear coupling strength approaches to twice the cavity frequency is observed with the help of new solutions in the limits.     

Deriving the New Traveling Wave Solutions for the Nonlinear Dispersive Equation,KdV-ZK Equation and Complex Coupled KdV System Using Extended Simplest Equation Method

In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.     

Analytical and Approximate Solutions for Complex Nonlinear Schrödinger Equation via Generalized Auxiliary Equation and Numerical Schemes

This article studies the performance of analytical, semi-analytical and numerical scheme on the complex nonlinear Schr¨odinger(NLS) equation. The generalized auxiliary equation method is surveyed to get the explicit wave solutions that are used to examine the semi-analytical and numerical solutions that are obtained by the Adomian decomposition method, and B-spline schemes(cubic, quantic, and septic). The complex NLS equation relates to many physical phenomena in different branches of science like a quantum state, fiber optics, and water waves. It describes the evolution of slowly varying packets of quasi-monochromatic waves, wave propagation, and the envelope of modulated wave groups, respectively. Moreover, it relates to Bose-Einstein condensates which is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero. Some of the obtained solutions are studied under specific conditions on the parameters to constitute and study the dynamical behavior of this model in two and three-dimensional.     

Energy Level and Riccati Equation

By an integral transformation, the energy eigenvalue problem of quantum bound state is converted to a nonlinear Riccati equation which is easily solved with the help of node theorem. Some typical examples are used to show the conciseness of this new approach.     

Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.     

Exact Solvability and Quantum Integrability of a Derivative Nonlinear Schrödinger Model

Using a variant of quantum inverse scattering method (QISM) which is directly applicable to field theoretical systems, we derive all possible commutation relations among the operator valued elements of the monodromy matrix associated with an integrable derivative nonlinear Schrödinger (DNLS) model. From these commutation relations we obtain the exact Bethe eigenstates for the quantum conserved quantities of DNLS model. We also explicitly construct the first few quantum conserved quantities including the Hamiltonian in terms of the basic field operators of this model. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This fact allows us to apply QISM to generate the spectrum of quantum DNLS Hamiltonian for the full range of its coupling constant.     

Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.