耗散子运动方程组的可控截断

为耗散子运动方程组提出精度可控的预截断方案来模拟和研究非微扰的量子耗散动力学．发展了具有类似Caldeira-Leggett主方程形式、在终止阶层采取马尔科夫和高温近似方法的截断方案,根据马尔科夫性质的分析给出确定终止层数的精度判据,并通过电荷转移体系的动力学模拟进行了检验．     

应用级联运动方程方法研究并联双量子点的量子纠缠（英文）

量子点体系是一类具有代表性的量子杂质体系.体系与环境之间的耗散过程和电子间的强相互作用对量子态的相干、纠缠有着极其重要的影响.多体效应和电子转移之间的竞争对局域自旋态之间的量子纠缠特性具有重要影响.本文应用级联运动方程方法对强关联双量子点系统的纠缠进行了定量研究.同时探究了总系统与子系统的信息熵之间的关系.     

随机薛定谔级联方程：理论和应用

随机薛定谔级联方程是一种基于波函数的严格量子动力学方法，它可用于研究耦合到玻色子热库的复杂体系中的量子动力学过程. 本综述从开放量子体系费曼路径积分的影响泛函出发，概述了随机薛定谔级联方程的一般理论框架和各种具体表述形式，并通过对复杂体系中超快激发能量转移过程的模拟来展示方法的应用范例和计算效率.     

量子Harper模型的量子计算鲁棒性与耗散退相干

运用量子轨迹和量子Monte Carlo仿真的方法,研究耗散退相干对周期驱动的量子Harper (quantum kicked Harper, QKH)模型量子计算的影响.数值仿真结果表明,一定强度的耗散干扰将破坏QKH特征状态的动态局域化以及相空间的随机网结构.以相位阻尼信道噪声模型为例分析了保真度的衰减规律以及可信计算时间尺度.与静态干扰相比,在干扰强度小于某一阈值时,耗散干扰下的可信计算时间尺度随量子比特的增加而快速下降;而在干扰强度大于该阈值时,静态干扰下的可信计算时间尺度下降更快. 关键词： 量子计算 量子Harper模型 主方程 量子Monte Carlo方法     

耗散子运动方程与福克-普朗克量子主方程

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,最近已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Harper模型的量子计算鲁棒性与耗散退相干

运用量子轨迹和量子Monte Carlo仿真的方法，研究耗散退相干对周期驱动的量子Harper (quantum kicked Harper, QKH)模型量子计算的影响.数值仿真结果表明，一定强度的耗散干扰将破坏QKH特征状态的动态局域化以及相空间的随机网结构.以相位阻尼信道噪声模型为例分析了保真度的衰减规律以及可信计算时间尺度.与静态干扰相比，在干扰强度小于某一阈值时，耗散干扰下的可信计算时间尺度随量子比特的增加而快速下降；而在干扰强度大于该阈值时，静态干扰下的可信计算时间尺度下降更快.     

耗散对受激拉曼绝热转移过程的影响

应用最近发展的量子耗散理论 ,研究了耗散对简单三能级体系的受激拉曼绝热转移过程的影响 ,并与pump dump过程比较 .计算结果表明 ,受激拉曼绝热转移的机制能很好地抑制中间态的弛豫与涨落的影响 .数值结果也表明了新的量子耗散理论可以正确地描述场与耗散相互耦合的动力学问题     

Paul阱中一维两离子系统的能带结构

利用熟知的级数截断方法，设计数值程序计算了线形Paul阱中库仑关联的两离子系统Schrdinger方程的精确解，得到接近目前离子阱实验能够实现的阱频下系统分立的运动态波函数和能谱，它们对应于阱频值的一个无穷可数的点集.在该点集内两相邻点之间连续变化阱频，由量子微扰法得到以精确分立谱为基础的能带结构，包括较宽的能隙和较窄的带宽.能带结构的存在将影响以该系统为基础的量子逻辑操作和激光边带冷却等问题，应该在实验研究中加以考虑.     

自旋团簇量子主方程的复合动力学对称性和热力学性质

基于三同核线型自旋团簇(每个粒子的自旋为S=1/2)的非自治量子主方程,研究了处于热辐射场中的自旋团簇的热力学性质.利用新颖的代数动力学方法,即引入动力学群的左右表象,不仅发现了自旋团簇的一个子空间态具有的SU(2)U(1)U(1)结构,而且对该子空间态在演化中所产生的耗散和退相干性质进行了计算.     

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.     

Adiabatic perturbations for compactons under dissipation and numerically-induced dissipation

Compacton propagation under dissipation shows amplitude damping and the generation of tails. The numerical simulation of compactons by means of dissipative schemes also show the same behaviors. The truncation error terms of a numerical method can be considered as a perturbation of the original partial differential equation and perturbation methods can be applied to its analysis. For dissipative schemes, or when artificial dissipation is added, the adiabatic perturbation method yields evolution equations for the amplitude loss in the numerical solution and the amplitude of the numerically-induced tails. In this paper, such methods are applied to the K(2,2)$K(2\text{,}2)$ Rosenau–Hyman equation, showing a very good agreement between perturbative and numerical results.     

Chaos in intrinsic motion of nuclei and its role in dissipative collective dynamics

We shall discuss the role of chaotic intrinsic motion in dissipative dynamics of the collective coordinates for nuclear systems. Using the formalism of linear response theory, it will be shown that the dissipation in adiabatic collective motion depends on the degree of chaos in the intrinsic dynamics of a system. This gives rise to a shape dependent dissipation rate for collective coordinates when the intrinsic motion is described by the independent particle model in a nucleus. The shape dependent chaos parameter measuring the degree of chaos in the intrinsic dynamics of the nuclear system will be obtained using the interpolating Brody distribution of nearest neighbour spacings in the single particle energy spectrum. A similar shape dependence is also found to be essential for phenomenological dissipation rates used in fission dynamics calculations.     

Analytical approach to the current correlation function in dissipative two-state systems

Using the spin-boson model with coupling to Ohmic bath, an analytical approach is developed to study the dynamics of the current correlation function in dissipative two-state systems with the view of understanding the effects of environment and tunneling on the coherent oscillation and the long-time decay of the current correlation function in these systems. An analytic expression of current correlation function is obtained and the results agree very well with that of numerical simulations.      

Nonlinear conductance fluctuations in a mesoscopic ring

We study the conductance of a single particle on a ring subject to an arbitrary dc electric field, which is generated by a linearly in time increasing magnetic flux. The full quantum mechanical time development is calculated numerically by splitting the dynamics into independent consecutive Zener tunneling transitions and free motion on the ring. The Zener transitions occur near the avoided crossings of the bandstructure which arises from the adiabatic eigenstates as a function of flux in the presence of a static scattering potential. To account for the necessary dissipation the particle is coupled to an appropriate oscillator bath which is adjusted to give a strictly linear current-voltage characteristic for arbitrary voltage and temperature in the absence of scattering. Taking a single δ-function scatterer we find that the dissipative coupling eliminates the localization in energy space found previously and leads to a well defined resistive steady state. The scattering introduces reproducible fluctuations around the average Ohmic behavior which are caused by coherent backscattering. Their magnitude depends on the strength of the scattering potential and decays slowly for large voltages. The associated correlation energy is determined by the uncertainty of the eigenstates due to the dissipative bath coupling. Thermal averaging leads to a decrease of the conductance fluctuations proportional to T^?1.     

Stability and instability of a hot and dilute nuclear droplet

Results on dissipative isoscalar modes of a hot and dilute nuclear droplet are presented. As compared to the adiabatic limit (part I), realistic dissipation yields a substantial reduction of the growth rates for all unstable modes, while the area of spinodal instability in the (ϱ,T)-plane remains unchanged. The qualitative features of multifragmentation through spinodal decomposition as obtained in the adiabatic limit are not significantly affected by dissipation. Received: 10 January 2002 / Accepted: 10 February 2002     

Correlated electrons in a dissipative environment

When a system of correlated electrons is embedded in a dissipative environment, new emergent phenomena might occur due to the interplay of correlation and dissipation. Here we focus on quantum impurity systems with coupling to a bosonic bath. For the theoretical investigation we introduce the bosonic numerical renormalization group method which has been initially set up for the spin-boson model. The role of both correlations and dissipation is described in the context of two-electron transfer systems. We also discuss prospects for the investigation of lattice models of correlated electrons with coupling to a dissipative bath.     

用Sin-DVR方法求解在绝热表象下锥形交叉分子振动本征态

在波恩-奥本海默近似中,分子中原子核的运动通常采用绝热表象的基态势能面来描述,一般情况下这样是比较好的近似. 然而当势能面上存在锥形交叉时,即使体系的能量远远低于锥形交叉点,绝热基态势能面近似将不再有效. 锥形交叉的出现,使得绝热表象下描述核运动的哈密顿中出现了两个额外的附加项：对角波恩－奥本海默近似校正(DBOC)项和几何相位(GP)项. 尤其GP项,使得基态绝热势能面近似失效. 这两项在锥形交叉点处的数值是发散的,因此在绝热表象中来严格描述核运动,会使量子动力学的计算存在数值收敛的困难. 在量子分子动力学计算中,最常用的数值方法是分离变量表象方法(DVR). 本文通过在绝热表象和透热表象下求解涉及两个电子态且包含锥形交叉的二维的薛定谔方程来验证Sinc-DVR的数值收敛性. 计算结果显示,在绝热表象中采用通常格点密度分布的Sinc-DVR方法,即使在没有特别的处理DBOC和GP项时,也可以得到比较可靠的结果. 此时的数值不确定性并没有比引入任意的向量势来纠正GP效应的不确定性更差. 需要特别注意的是,纠正GP效应的任意向量势的精确形式,通常是不易得到其精确形式的.     

Shot noise spectrum of open dissipative quantum two-level systems

We study the current noise spectrum of qubits under transport conditions in a dissipative bosonic environment. We combine (non-)Markovian master equations with correlation functions in Laplace space to derive a noise formula for both weak and strong coupling to the bath. The coherence-induced reduction of noise is diminished by weak dissipation and/or a large level separation (bias). For weak dissipation, we demonstrate that the dephasing and relaxation rates of the two-level systems can be extracted from noise. In the strong dissipation regime, the localization-delocalization transition becomes visible in the low-frequency noise.     

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F=-ηV(2); (iii) F=-ηV(μ) with μ≠1 and μ≠2 and; (iv) F=-ηV, where η is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined.