自由高斯波包在量子相空间中的动力学研究

在Tortes—Vega和Frederick（简称T-F）量子相空间的理论框架下,将波函数表示成相应的极化形式,给．出了量子相空间中的含时Schrodinger方程的另一种等价表示形式,并且利用这种方法数值求解了自由高斯波包在相空间中的演化行为,对得到的结果进行了讨论,以期用这种方法探索更为实际和复杂的体系在量子相空间中的演化行为。     

一维中心势V(q)=Bq2+A/q2(A, B>0)中运动的粒子在量子相空间表示中的解

在Torres-Vega 和 Frederick(T-F)量子相空间理论的框架下, 求解了相空间中一维中心势场V(q)=Bq2+A/q2(A, B>0),中运动的单粒子的本征函数, 并对相空间中的概率密度函数进行了讨论.     

GW方法: 基本原理, 最新进展及其在d-和f-电子体系中的应用

基于格林函数的多体微扰理论提供了描述材料基态和激发态性质的一个严格理论框架. 格林函数依赖于交换关联自能, 后者满足一组复杂的被称为Hedin方程的积分微分方程. GW方法是由对自能算符根据屏蔽库仑作用做多体微扰理论展开到第一项得到, 是目前描述扩展体系准粒子电子激发性质最为准确的第一原理方法. 本文概述了GW方法的基本原理, 并对最新的理论方法进展在一个统一的框架下进行了评述. 最后, 通过对若干典型实例的分析展示了针对d/f-电子体系的GW方法的现状.     

路径积分刘维尔动力学方法的进一步探讨

计算分子体系的量子时间关联函数为人们理解预测其动力学过程提供了有力的理论工具.本文立足于魏格纳相空间,回顾了平衡刘维尔动力学、平衡连续性动力学和平衡哈密顿动力学这3种相空间量子动力学方法.它们可以保证平衡系统热力学物理量不随时间变化并给出任意算符的时间关联函数的经典、高温或谐振子极限.在速度分布满足全局高斯分布的条件下,3种相空间量子动力学方法可以推导出相同的运动方程.利用虚时间路径积分来表示该运动方程的有效力,并对路径积分珠子做Staging变换,利用分子动力学来对路径积分珠子位置空间进行取样,我们可以推导出路径积分刘维尔动力学.本文分析指出,当路径积分刘维尔动力学和应用白噪声的朗之万动力学控温方法结合,如果朗之万摩擦系数和路径积分刘维尔动力学中的绝热频率相等,在自由粒子极限下对路径积分珠子位置空间进行取样的效率最高,可以作为最优朗之万摩擦系数的建议值.本文还建议了一种更高效的算法来演化路径积分刘维尔动力学的轨线.     

苯的振动量子能级的非线性量子理论计算

用最近发展起来的非线性量子学的定态本征方程的理论去计算蒸气和液体的苯（Ｃ６Ｈ６）和重苯（Ｃ６Ｄ６）的ＣＨ和ＣＤ键的振动所产生的量子能态，同时用非线性简并微扰理论计算在弱色散极限下苯的稳定的能态劈裂，得到较为满意的结果。     

基于密度泛函理论研究二元排斥Yukawa流体的表面结构性质

基于自由能密度泛函理论(DFT)考察了二元排斥Yukawa (HCRY)流体在不同外场下的密度分布. 基于微扰理论, 体系的Helmholtz自由能泛函采用硬球排斥部分和长程色散部分贡献之和, 其中Kierlik和Rosinberg的加权密度近似(WDA)被用来计算硬球排斥部分, 而色散部分采用平均场理论(MFT)进行描述. 为了验证DFT计算结果的合理性, 研究中采用巨正则Monte Carlo(GCMC)模拟计算了在不同主体相密度、硬核直径和位能参数比的条件下二元HCRY混合流体的密度分布. 结果表明, 该DFT计算结果与GCMC模拟值吻合良好.     

含时密度矩阵重正化群的理论与应用

密度矩阵重正化群(DMRG)作为计算低维强关联体系强有力的方法为人熟知, 在量子化学电子结构计算中得到广泛应用. 最近几年, 含时密度矩阵重正化群(TD-DMRG)的理论取得较快发展, TD-DMRG逐渐成为复杂体系量子动力学理论模拟的重要新兴方法之一. 本文综述了基于矩阵乘积态(MPS) 和矩阵乘积算符(MPO)的DMRG基本理论, 并重点介绍了若干最常见的TD-DMRG时间演化算法, 包括基于演化再压缩(P&C) 的算法、 基于含时变分原理(TDVP)的算法和时间步瞄准(TST)算法; 还对利用TD-DMRG模拟有限温体系的纯化(Purification)算法和最小纠缠典型量子热态(METTS)算法进行了介绍. 最后, 对近年TD-DMRG在复杂体系量子动力学中的应用进行了总结.     

频域空间密度矩阵重正化群的研究进展

密度矩阵重正化群(DMRG)作为低维强关联体系中电子结构计算的强有力方法被广泛熟知, 并被迅速地应用于量子化学, 不仅在电子结构计算中发挥重要作用, 同时也在近几年迅速地成为复杂体系量子动力学计算的重要方法. 在DMRG框架中, 衍生出了一系列计算动态响应性质的有效方法, 并得到了广泛应用. 本文简述了DMRG的基本理论, 其矩阵乘积态(MPS)表示有效地扩展了该方法的应用范围. 重点介绍了基于线性响应理论的动态DMRG, 在频率空间求解系统在零温以及有限温度下响应性质的算法, 并介绍其在电子关联问题和电子-声子关联问题中的应用, 最后展望了该领域的未来发展方向.     

用解析Ross变分微扰理论研究蛋白质盐溶液的渗透压

采用软球三Yukawa势代替文献中的硬核双Yukawa势描述带电蛋白质分子之间的色散吸引、色散排斥和屏蔽静电排斥作用, 采用Ross变分微扰理论推导出解析状态方程(EOS), 克服了文献中常用的平均球近似对多Yukawa势存在的困难. 应用新理论研究了牛血清蛋白(BSA)-NaCl水溶液在不同pH值、不同浓度下的渗透压. 结果表明该理论独立参数的个数仅比林阳政等人最近提出的理论多一个, 而精确度有很大提高. 分析表明, 对于分子量大的蛋白质溶液体系采用新的软球理论比硬球理论会有明显的改进.     

非平衡体系-热库纠缠定理与热输运

将最近建立的体系-热库纠缠定理(SBET)扩展到非平衡的情形. 其中, 任意体系与处于不同温度的多个高斯型热库环境相耦合. 现有的SBET将体系-热库的纠缠响应函数与体系的局域响应函数联系起来, 而扩展的理论则关注通过分子结的非平衡稳态量子输运流. 新理论是基于广义Langevin方程建立的, 它与量子情形下的非平衡热力学密切相关.     

Solution of the “Classical” Schrödinger equation for a driven symmetric triple well: A comparison with its classical counterpart

The behavior of a driven symmetric triple well potential has been studied by developing an algorithm where the well‐established Bohmian mechanics and time‐dependent Fourier Grid Hamiltonian method are incorporated and the quantum theory of motion (QTM) phase space structures of the particle are constructed, both in “nonclassical” and “classical” limits. Comparison of QTM phase space structures with their classical analogues shows both similarity as well as dissimilarities. The temporal nature and the spatial symmetry of applied perturbation play crucial roles in having similar phase space structures. © 2016 Wiley Periodicals, Inc.     

Topology of the distribution of zeros of the Husimi function in the LiNC/LiCN molecular system

Phase space representations of quantum mechanics constitute useful tools to study vibrations in molecular systems. Among all possibilities, the Husimi function or coherent state representation is very widely used, its maxima indicating which regions of phase space are relevant in the dynamics of the system. The corresponding zeros are also a good indicator to investigate the characteristics of the eigenstates, and it has been shown how the corresponding distributions can discriminate between regular, irregular, and scarred wave functions. In this paper, we discuss how this result can be understood in terms of the overlap between coherent states and system eigenfunctions.     

Husimi representation for stationary states

This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.     

Quantum evolution speed and its limit in the driven double-well system

We investigate quantum evolution speed in the driven double-well system using the entangled trajectory molecular dynamics method. We emphasize not only the evolution speed of the quantum state but also its limit according to different definitions. The Wasserstein 1-distance is used to quantify the distance between distinguishable quantum states in the phase space, the quantum speed limit based on the geometry has been shown to be the strictest one. The single trajectory's contribution to the quantum speed limit is discussed, which is related to both the time evolution of the trajectory and its position in the total Wigner function. The resonance and chaos strongly enhance the evolution speed and its limit in the driven double-well system. The resonance effect makes a large proportion of representative points pass through the well as a whole, nevertheless, the chaos makes the Wigner function disperse in the phase space.     

Ivar Waller 90 years on June 11, 1988

Linkage properties of the diagrammatic representation of the energies obtained in the multireference many-body perturbation calculations with respect to the incompleteness or completeness of the model space are discussed. The case of not completely degenerate model space is considered for which a comparison with the standard single-reference many-body perturbation expansion is possible. The Hose–Kaldor type of graphical representation of the perturbation expansion for the effective Hamiltonian is used in this comparison. It is shown that for an incomplete model space the perturbation expansion is not size-extensive. In this case, for a truncated expansion of the effective Hamiltonian, the energies obtained by diagonalization of the effective Hamiltonian matrix are represented by both linked and unlinked irreducible contributions. The unlinked ones do not appear when the complete model space is used.     

Contracted Schrödinger equation in quantum phase‐space

The phase space formulation of quantum mechanics is equivalent to standard quantum mechanics where averages are calculated by way of phase space integration as in the case of classical statistical mechanics. We derive the quantum hierarchy equations, often called the contracted Schrödinger equation, in the phase space representation of quantum mechanics which involves quasi‐distributions of position and momentum. We use the Wigner distribution for the phase space function and the Moyal phase space eigenvalue formulation to derive the hierarchy. We show that the hierarchy equations in the position, momentum, and position‐momentum representations are very similar in structure. © 2017 Wiley Periodicals, Inc.     

Semiclassical initial value treatment of correlation functions

Two semiclassical, initial value representation (IVR) treatments are presented for the correlation function psi(f) e-iHt/h psi(i), where psi(i) and psi(f), are energy eigenfunctions of a "zero-order" Hamiltonian describing an arbitrary, integrable, vibrational system. These wave functions are treated semiclassically so that quantum calculations and numerical integrations over these states are unnecessary. While one of the new approximations describes the correlation function as an integral over all phase space variables of the system, in a manner similar to most existing IVR treatments, the second approximation describes the correlation function as an integral over only half of the phase space variables (i.e., the angle variables for the initial system). The relationship of these treatments to the conventional Herman-Kluk approximation for correlation functions is discussed. The accuracy and convergence of these treatments are tested by calculations of absorption spectra for model systems having up to 18 degrees of freedom, using Monte Carlo techniques to perform the multidimensional phase space integrations. Both treatments are found to be capable of producing spectra of excited, anharmonic states that agree well with quantum results. Although generally less accurate than full phase space or Herman-Kluk treatments, the half phase space method is found to require far fewer trajectories to achieve convergence. In addition, this number is observed to increase much more slowly with the system size than it does for the former methods, making the half-phase space technique a very promising method for the treatment of large systems.     

Trial introduction of a complex potential function for perturbation that causes quantum mechanical transition in a one‐dimensional harmonic oscillator

Some results of computer simulation of the behavior of a one‐dimensional quantum mechanical oscillator are reported in this article. This harmonic oscillator comprises a particle trapped within a hyperbolic potential V(x) = x². Further, a perturbation potential function V′(x, t) was superposed upon the hyperbolic potential in order to induce a quantum mechanical transition. This perturbation function V′(x, t) is a function of both of space and time variables, and is set to represent a wave packet that is enveloped by a Gaussian bell‐shaped curve. A wave that probably has an appropriate wave number and angular frequency was inputted into the expression for the wave packet. In the initial phase, while the harmonic oscillator was allowed to oscillate almost freely, the wave packet was allowed to approach the harmonic oscillator. In the middle phase, the wave packet passes through the harmonic oscillator, affecting the shape of the quantum mechanical wave that represents the physical state of the system. In the last phase, when the wave packet left the system of the harmonic oscillator, the system settled onto an energetically stable state. The main objective of the simulation was to simulate the instance of a quantum mechanical transition from one eigenstate to another. After several trials, it was found that the perturbation function consisting of a complex function was, at least superficially, able to cause one desired transition, that is, a transition from one eigenstate to another eigenstate. By using such a complex perturbation function, a transition from the first excited state to the ground state was observed to occur. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004