Physical Features of Binary Coulomb Crystals: Madelung Energy,Collective Modes and Phonon Heat Capacity

Electrostatic energy, collective modes, and thermodynamic functions of a Coulomb crystal with equal number of ions of two different types and uniform charge‐compensating electron background are studied using harmonic lattice model. Simple cubic and hexagonal lattices with two different ions in the elementary cell (we denote these lattices sc2 and h2, respectively) are considered. The static sc2 lattice is more tightly bound than the h2 one at any charge ratio of the constituent ions. The phonon spectra depend on the ion charge and mass ratio. An analysis shows that these binary Coulomb crystals are stable, if the charge ratio is not too different from 1 (about 3.6 for sc2 and 1.3 for h2 lattices) regardless of the mass ratio. Heat capacity of the sc2 lattice is obtained by numerical integration over the first Brillouin zone as a function of temperature and charge and mass ratios. Well known classic and quantum asymptotes of the heat capacity are reproduced, and the dependence of the coefficient in the Debye T³ law on charge and mass ratios is presented (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffusion in lattice Lorentz gases : Nearest scatterers approximation

The expressions for diffusion coefficients and for velocity autocorrelation functions of lattice Lorentz gases are derived both in the nearest scatterers and Boltzmann approximations. The results are obtained for linear chain, square, triangular, simple cubic, body centred cubic, face centred cubic and face centred hyper cubic lattices. The diffusion coefficients are compared with those from the effective medium approximation for the square lattice and with computer simulation results for triangular, simple cubic and body centred cubic lattices.     

布里渊区中的对称平均点

本文提出了一些布里渊区中的对称平均点,用它可以方便地计算布里渊区中的平均值,其精度可以和特殊点相比而计算量却要小得多。文内给出了立方和六角晶格的对称平均点,并用具体的数值计算例子说明了它的计算精度。 关键词：     

Special points for calculating integrals over the primitive cell of a periodic system

A method is proposed for constructing appropriate sets of special points in the Brillouin zone in which the extended unit cell method is used with a subsequent shift from the center of the reduced Brillouin zone. The proposed method offers several advantages over the commonly used Monkhorst-Pack method. The difference in the construction of sets of special points for the direct and reciprocal lattices is discussed for crystals belonging to a nonsymmorphic space group. The cases of a planar square lattice and an fcc lattice are considered to illustrate general results.     

On the Callen and Shtrikman approach to the theory of magnetic anisotropy and magnetostriction

Two different methods are applied to the Callen and Shtrikman theory of magnetic single-ion anisotropy. The first method exploits an explicit inversion of the Brillouin function for values of spin not greater than two. The second method is equivalent to a parametric inversion of the Brillouin and the Langevin functions and is effective for any value of spin. Both methods allow the easy generation of the anisotropy coefficients as functions of the magnetization which can then be taken either from any of the theories of the general class defined by Callen and Shtrikman or from experiment. Extension of the results to the case of strong crystal field anisotropy is possible. The parametric method itself is much wider in scope; several promising applications in related fields are pointed out.     

Brillouin zone spectroscopy of nonlinear photonic lattices

We present a novel, real-time, experimental technique for linear and nonlinear Brillouin zone spectroscopy of photonic lattices. The method relies on excitation with random-phase waves and far-field visualization of the spatial spectrum of the light exiting the lattice. Our technique facilitates mapping the borders of the extended Brillouin zones and the areas of normal and anomalous dispersion within each zone. For photonic lattices with defects (e.g., photonic crystal fibers), our technique enables far-field visualization of the defect mode overlaid on the extended Brillouin zone structure of the lattice. The technique is general and can be used for photonic crystal fibers as well as for periodic structures in areas beyond optics.     

钽激光等离子体的自电离和辐射衰减特性(英文)

在自旋轨道劈裂阵模型下,考虑组态间的耦合,计算出类铜钽激光等离子体的跃迁组态的波长和对应的波数,通过组态平均分析了其自电离与辐射跃迁特性,得出相关的自电离系数和辐射衰减系数,这些参数为分析高离化钽激光等离子体的双电子复合过程提供了重要的理论依据.     

The XXZ Heisenberg model on random surfaces

We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.     

Generalized Brillouin theorem and generalized forces in SCF and MC SCF theories and their Hartree-Fock limits

A formula for the change of energy is derived, valid for any infinitesimal change of the hamiltonian and the wave function in CI, SCF and MC SCF theories. A general form of MC Hartree-Fock equations is derived in a somewhat new form. A closed MC theory is defined and a condition of self-consistency is derived for this theory. The role of deorthogonalization of spin orbitals is discussed. The Hellmann-Feynman theorem and the generalized Brillouin theorem are rederived in a unique and simple way. It is shown that in the case of the closed MC SCF theory the Brillouin theorem derived by Levy and Berthier can be strengthened.

Formulae for generalized forces are derived, valid for closed-shell, openshell and multiconfigurational SCF theories also far from the Hartree-Fock limit.     

Zone structure and its genesis from the states of sublattices in orthorhombic MgGeN<Subscript>2</Subscript>

It is demonstrated that the crystalline structure of MgGeN₂ can be reduced to the superposition of “approximated” high-symmetry Bravais sublattices by shifting atoms in a unit cell within the range of 5% of the lattice constant. The superimposed Brillouin zones were plotted for crystal lattices and sublattices. The computational results are presented for the electronic structure of MgGeN₂ in terms of the theory of the density function. The influence of “hidden” symmetry in this crystal on zone spectra is described.     

位势问题改进的无网格局部Petrov-Galerkin法

将滑动Kriging插值法与无网格局部Petrov-Galerkin法相结合,采用Heaviside分段函数作为局部弱形式的权函数,提出改进的无网格局部Petrov-Galerkin法,进一步将这种无网格法应用于位势问题,并推导相应的离散方程.因为滑动Kriging插值法构造的形函数满足Kronecker函数性质,所以本文建立的改进的无网格局部Petrov-Galerkin法可以像有限元法一样直接施加边界条件;由于采用Heaviside分段函数作为局部弱形式的权函数,因此在计算刚度矩阵时只涉及边界积分,而没有区域积分.此外,还对本方法中一些重要参数的选取进行了研究.数值算例表明,本文建立的改进的无网格局部Petrov-Galerkin法具有数值实现简单、计算量小以及方便施加边界条件等优点.     

Berry phase in magnetic superconductors

In magnetic systems, electronic bands often acquire nontrivial topological structure characterized by gauge flux distribution in momentum k space. It sometimes follows that the phase of the wave functions cannot be defined uniquely over the whole Brillouin zone. In this Letter, we develop a theory of superconductivity in the presence of this gauge flux both in two- and three-dimensional systems. It is found that the superconducting gap has "nodes" as a function of k where the Fermi surface is penetrated by a gauge string.     

Scattering of waves by irregularities in periodic discrete lattice spaces. I. Reduction of problem to quadratures on a discrete model of the Schrödinger equation

The scattering of plane waves and of point source pulses by irregularities in a discrete lattice model of the Schrödinger equation is considered. Closed form expressions are derived for the scattered wave function in terms of lattice Green's functions in the case that a finite number of lattice points or “bonds” are defective. The scattered wave function appears in the form of the ratio of two determinants. While in continuum scattering theory the scatterer must have some symmetry, perhaps spherical, cylindrical or elliptical, in order to allow separation of variables in the basic scattering differential equation, such symmetries are not necessary for the construction of scattered wave functions on discrete lattices. When the number of irregularities becomes large, the determinants in the solution of the scattering problem become large.     

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

Abstract

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.     

Finite diffraction models for electron bandstructures

Truncations of the infinite determinant resulting from the plane wave expansion method for an electron in a periodic potential are analysed to determine how well they can reproduce the low-lying eigenvalues or energy bands. The availability of rigorous expansions for the solutions of the Mathieu equation, essentially the Schrödinger equation for an electron in a one-dimensional cosine potential, suggests that problem for definitive comparisons. Since the only models which can reproduce the fundamental quadratic behaviour of bands at the zone centre have symmetric (odd) sets of reciprocal lattice vectors, the lowest order candidate has an odd determinant of size 3 × 3 through the reciprocal lattice vectors which define the 1st. Brillouin zone of the one-dimensional lattice. As zone centred determinants are not symmetric about zone boundaries they will not give a vanishing group velocity at that point and the effects of truncation will be at their worst. The 3 × 3 or cubic model factorises at the zone centre and a detailed analysis in closed form is straightforward. Agreement with the rigorous results is better than 1% everywhere. The next largest model, with a 5 × 5 determinant, gives errors which are several orders of magnitude smaller throughout the 1st. Brillouin zone. In addition it is found that even the 3 × 3 model gives much better results for the lowest eigenvalue than does second order perturbation theory. Numerical comparisons are also made for the group velocity and (inverse) effective mass using a Hellman-Feynmann approach to calculate the derivatives. Extensions to complex periodic potentials and higher dimensions are briefly discussed.     

Temporal integration of trains of tone pulses by normal and by cochlearly impaired listeners

Two experiments investigated the temporal integration of trains of tone pulses by normal and by cochlearly impaired listeners. In the first experiment, thresholds were measured for a single 5-ms, 4-kHz tone pulse, and for ten such tone pulses as a function of interpulse interval (delta t). For normal listeners, temporal integration, defined as the threshold difference between one and ten pulses, was about 8 dB for delta t less than 20 ms, and about 5 dB at longer delta t's. For impaired listeners, temporal integration was only about 2-3 dB across the range of delta t's (5-160 ms) studied. A second experiment measured psychometric functions (log d' versus log signal power) for a single pulse and for ten pulses with delta t's of 5 ms and 80 ms. The normal listeners' functions had slopes close to unity in all three conditions, with a few exceptions. The impaired listeners' functions had slopes close to unity for ten pulses with delta t = 5 ms, but had slopes significantly greater than unity for delta t = 80 ms, and for a single pulse. At delta t = 80 ms, the increase in d' relative to the condition with a single tone was similar (a factor of square root of 10) for both impaired and normal listeners, but the threshold difference was smaller for the impaired listeners due to their steeper psychometric functions. For impaired listeners, then, temporal integration at delta t = 80 ms was normal in terms of a change in d' but abnormal when measured as a threshold difference.(ABSTRACT TRUNCATED AT 250 WORDS)     

A technique for analytical calculation of observables in lattice gauge theories

It is shown that the partition function for a finite lattice factorizes into terms that can be associated with each vertex in the finite lattice. This factorization property forms the basis of a well-defined and efficient technique developed to calculate partition functions to high accuracy, on finite lattices for gauge theories. This technique, along with an expansion in finite lattices, provides a powerful means for calculating observables in lattice gauge theories. This is applied to SU(2) lattice gauge theory in four dimensions. The free energy, expectation value of a plaquette and specific heat are calculated. The results are very good both in the strong coupling and the weak coupling region and describe the crossover region quite well, agreeing all the way with the Monte Carlo data.     

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 non-isotropic two-dimensional random walk

A formula is obtained for the joint probability density function of the angle and length of the resultant of an N-step non-isotropic random walk in two dimensions for arbitrary step angle and radius probability density and for any fixed number of steps. The problem is attacked by applying the theory of generalized functions concentrated on smooth manifolds. The analysis is presented initially for the case where only the angles are random. The characteristic function is defined for the walk in terms of angular and radial frequencies and the inversion is obtained in terms of a sum of Hankel transforms. The Hankel transform sum is transformed by showing that it can be interpreted in terms of the motions of the two-dimensional Euclidean plane corresponding to the rotations and translations resulting from a sequence of fixed steps. This transformation results in an expression involving integrations over two manifolds defined by delta functions. The properties of the manifolds defined by the delta functions are then considered and this results in some simplification of the formulae. The analysis is then generalized to the case where both the phase and length of each step in the walk are random. Finally, seven examples are presented including the general two-step walk and three walks which lead to generalized K density functions for the resultant.     

复合函数算符的微商法则及其在量子物理中的应用

给出了在量子物理学、量子统计学、算符排序理论、矩阵论以及控制理论中有着重要用途的复合函数算符的一般微分法则,利用这一法则研究了Wigner算符和Weyl对应规则中的积分问题,证明了两类典型的算符恒等公式.给出了Wigner算符的有序算符内的微分形式,并得到了一些重要函数的新的微分式.最后,引入了一个参数型的Wigner算符来统一正规序、Weyl编序以及反正规序三种算符排序.