Mean fields and self consistent normal ordering of lattice spin and gauge field theories

Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived.     

The heavy fermion damping rate puzzle

We examine again the problem of the damping rate of a moving heavy fermion in a hot plasma within the resummed perturbative theory of Pisarski and Braaten. The ansatz for its evaluation which relates it to the imaginary part of the fermion propagator pole in the framework of a self-consistent approach is critically analyzed. As already pointed out by various authors, the only way to define the rate is through additional implementation of magnetic screening. We show in detail how the ansatz works in this case and where we disagree with other authors. We conclude that the self-consistent approach is not satisfactory.     

二元无规混合系统的有效介质理论

本文从二元无规混合物的两种不同拓扑结构出发,在Maxwell-Garnett理论的基础上,提出一种自洽的方法以改进类平均场的Bruggeman有效介质理论。导出了二元无规混合物有效电导率的普适式,研究了一些实际材料的电导率和热导率问题,理论计算结果与实验数据符合甚好。 关键词：     

Modelling and Simulation of Magnetron Infection Guns for Submillimeter Wave Gyrotrons

The software package GUN-MIG has been developed for computer simulation of beam formation in magnetron injection guns (MIG). It is based on a fully relativistic self-consistent physical model which takes into account the specific problems and requirements that are being encountered in the analysis and design of MIG for gyrotrons. Besides providing a general outline of the physical models and the program implementation of the code, several illustrative examples of the numerical experiments with real MIG for submillimeter wave gyrotrons are presented and discussed.     

Disorder scattering in magnetic tunnel junctions: theory of nonequilibrium vertex correction

We report a first principles formalism and its numerical implementation for treating quantum transport properties of nanoelectronic devices with atomistic disorder. We develop a nonequilibrium vertex correction (NVC) theory to handle the configurational average of random disorder at the density matrix level so that disorder effects to nonlinear and nonequilibrium quantum transport can be calculated from atomic first principles in a self-consistent and efficient manner. We implement the NVC into a Keldysh nonequilibrium Green's function (NEGF) -based density functional theory (DFT) and apply the NEGF-DFT-NVC formalism to Fe/vacuum/Fe magnetic tunnel junctions with interface roughness disorder. Our results show that disorder has dramatic effects on the nonlinear spin injection and tunnel magnetoresistance ratio.     

Self-consistent normal ordering of gauge field theories

Mean field theories with a real action of unconstrained fields can be self-consistently normal ordered. This leads to a considerable improvement over standard mean-field theory. This concept is applied to lattice gauge theories. We construct first an appropriate real action mean-field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean-field theory are derived.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Bose-Einstein condensation quantum kinetics for a gas of interacting excitons

A quantum kinetics of the Bose-Einstein condensation in the self-consistent (s.c.) Hartree-Fock-Bogoliubov (HFB) model of the interacting Bose gas is formulated and numerically solved for the example of excitons scattering with a thermal bath of acoustic phonons. The theory describes the condensation in real time starting from a nonequilibrium initial state towards the equilibrium HFB solution. The s.c. changes of the spectrum are automatically incorporated in the scattering terms.     

Quantum decision theory as quantum theory of measurement

We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities nonadditive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems.     

KSSOLV-GPU：一款利用GPU高效求解Kohn-Sham方程的平面波基组密度泛函理论MATLAB程序包

KSSOLV(Kohn-Sham Solver)是一款用于求解平面波基组下Kohn-Sham方程(KS-DFT)的MATLAB(Matrix Laboratory)工具箱. 在KS-DFT的基态计算中,通常自洽场迭代中Kohn-Sham哈密顿量的对角化是最昂贵的部分. 为了使得个人计算机也能够执行数百个原子的中等大小KS-DFT计算,本文提出了一种CPU-GPU的混合编程方案,通过调用MATLAB内置的并行计算工具箱来加速在KSSOLV中实现的迭代对角化算法. 比较了KSSOLV-GPU在RTX3090、V100、A100三种GPU上的性能;结果表明,对于包含128个原子的块状硅体系,与串行的CPU计算相比,混合CPU-GPU的编程可以实现约10倍的加速. 特别是其在最新的民用GPU显卡RTX3090上也具有优秀的表现,可以预想到在不远的将来,KSSOLV-GPU借助MATLAB强大的可视化能力与GPU的加速支持可以在一台配备了民用GPU显卡的个人电脑上实现常规的DFT计算分析与可视化,从而降低了材料模拟与计算领域的门槛.     

Aspects of Green's function methods versus self-consistent field theory

The basic methods of solving fully symmetric, nonlinear theories are stated. These are discussed in terms of Green's function methods and self-consistent field theory methods. The equivalence of many-body theory based on Green's functions with quantum field theory, on which the self-consistent field theory is based, is reviewed. A number of similarities, differences, and cautions involved with these methods are determined. In particular, since very often both methods are based upon use of the adiabatic theorem, which is typicallynot applicable to the models under consideration, a deviation in the self-consistent theory is discussed that avoids this problem. A similar idea is used for solution of models with the functional integral method. Ferromagnetic models are used at various places in illustrating some of the ideas. By contrasting these methods further insight may be gained into solving nonlinear, physical theories.     

光学无源谐振腔的矩阵理论(柱坐标)(Ⅰ)——自洽场矩阵方程

本文讨论了文献中提出的根据标量光波传播矩阵理论的光学无源谐振腔自洽场矩阵方程。提出了对自洽场性质的新认识、元模转换概念和自洽场元模结构分析方法。在普遍情况下,严格证明了上述矩阵方程可截取为有穷阶以求近似解。给出了确定上述有穷阶矩阵方程本征值误差上限的严格公式。还给出了估算由该方程导出的所有结果的计算误差上限的较为方便的公式与方法。本文提出的光学无源谐振腔的矩阵理论较方便于各阶横模,包括那些模损耗相当近于1的高阶横模的计算。作者认为这个理论还应该较适合于复杂谐振腔的分析和计算。由于所用坐标系的关系,本文所提出的理论仅适用于理想轴对称性系统。 关键词：     

Relativistic description of single-particle resonances via phase shift analysis

Single-particle resonant states in spherical nuclei are studied by the real stabilization method in coordinate space within the framework of self-consistent relativistic mean field theory. Taking 122Zr as an example, the resonant parameters, including the energies and widths are extracted by fitting energy and phase shift. Good agreement with the previous calculations has been found. The details of single-particle resonant states are analysed.     

Relativistic description of single-particle resonances via phase shift analysis

Single-particle resonant states in spherical nuclei are studied by the real stabilization method in coordinate space within the framework of self-consistent relativistic mean field theory. Taking 122Zr as an example, the resonant parameters, including the energies and widths are extracted by fitting energy and phase shift. Good agreement with the previous calculations has been found. The details of single-particle resonant states are analysed.     

Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables ρ, the number density, and B, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.     

Relaxation in time-dependent current-density-functional theory

We apply the time-dependent current-density-functional theory to the study of the relaxation of a closed many-electron system evolving from a nonequilibrium initial state. We show that the self-consistent unitary time evolution generated by the exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system, i.e., the noninteracting system whose particle and current densities coincide with those of the physical system under study, is related to the entropy production in the real system.     

Contact effect in the dynamic electron transport of a two-probe mesoscopic conductor

Based on the self-consistent electron dynamic transport theory for multi-probe mesoscopic systems, we calculate the distribution of internal potential, charge density, and ac conductance of a two-probe mesoscopic conductor with wide trapezoid reservoirs, and study the contact effect. The results show that including the contact effect can make a significant difference to the frequency-dependent electron transport properties. In the nonzero frequency case, the internal potential and the charge density are complex with extremely small imaginary parts. Importantly, the imaginary part of the charge density gives rise to a real ac conductance (admittance), which corresponds to the charge-relaxation resistance.     

毫米波回旋速调管放大器的自洽非线性数值模拟

为了实现回旋速调管放大器的快速设计,基于经典的回旋管的稳态单模非线性理论方法,开展了回旋速调管放大器的束波作用效率的理论模拟研究。由于单模理论无法匹配回旋速调管放大器的输入腔、中间腔两端的突变边界条件,所以输入腔与中间腔都只能采用给定场法进行求解。回旋速调管的输出腔的功率输出端通常采用缓变结构,这种腔体可以采用单模自洽理论进行求解。对两腔毫米波回旋速调管放大器进行了理论模拟,并与商业粒子模拟软件的结果进行对比,验证了该数值理论模拟方法的有效性。     

Multiple band electron-phonon transport theory: I. Generating functional approach and generalized response

For an electron-phonon system with several equivalent bands a generalized transport and response theory is derived which serves as microscopic justification of a model for the structural phase transition in A15-compounds. By means of a generating functional approach a self-consistent formulation of the theory is achieved. The resulting set of coupled integral equations becomes closed within the ladder approximation. In particular, the functional formalism is used to calculate the generalized response occuring in a coupled electron-phonon system. In a subsequent paper a self-consistent solution of the coupled equation will be given with which the response functions are evaluated and discussed with recourse to the particularities of A15-compounds.