Electron-phonon interactions in bct white tin

The electron-phonon interactions are evaluated exactly over the actual shape of the atomic polyhedron as well as the lattice polyhedron of diatomic white tin by making use of simple coordinate axes transformations and crystal symmetry. It is shown that the expressions for the interference factor,S(q, t) of the atomic polyhedron are complex while those for the lattice polyhedron are real and the reciprocal lattice vectors derived from the former do not correspond to those derived either from the latter or from x-ray structure factors. By comparing these expressions with each other as well as with those obtained by approximating these polyhedra by an ellipsoid of equivalent volume, apparent differences between the interference factors of atomic and lattice polyhedra, consequent ambiguity regarding the shape and size of the first Brillouin zone of white tin, validity of the Wigner-Seitz approximation for a diatomic lattice and the manner in which the electron-phonon interactions contribute to acoustical and optical modes of vibration are discussed.     

Interpretation of the isomer shift of interstitially implanted119Sn impurities in group IV semiconductors

Recent Mössbauer measurements of the isomer shift of interstitially implanted¹¹⁹Sn impurities in group IV semiconductors are interpreted in terms of the electron contact density of compressed Sn atoms and ions, respectively. The finite space allowed to the impurity atom in the host crystal is approximated by a Wigner-Seitz sphere. Using a calibration procedure, the dependence of the isomer shift on the Wigner-Seitz radiusR _A has been calculated for several electron configurations of the tin atom (ion). The isomer shift values for¹¹⁹Sn interstitials in diamond, silicon, germanium, and -tin are found to correspond to compressed, neutral tin atoms; furthermore, the relaxation of the host lattice about the impurity Sn atom is discussed.     

Electron-ion interactions in close packed metals

The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron by making use of simple co-ordinate axes transformations and lattice symmetry in the case of hcp and ccp structures. It is shown that the expressions for the interference factor,S(q,t) of hcp structure are complex while those of ccp structure are real, even when both atomic arrangements are referred to the same orthorhombic co-ordinate axes, and in each case, lattice atom contributions could be distinguished from basis atom contributions toS(q,t). By comparing these expressions with each other as well as with those obtained by approximating their atomic polyhedra by an ellipsoid of equivalent volume, apparent differences between interference factors of hcp and ccp structures, validity of Wigner-Seitz approximation for a diatomic lattice and the manner in which the electron-ion interactions contribute to the different modes of vibration in a hexagonal lattice are discussed.     

The electron-ion interactions in tetragonal metals

The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron, instead of approximating it by a sphere or an ellipsoid, by making use of simple co-ordinate axes transformations and lattice symmetry in the case of fct and bct structures. It is shown that there are several alternative ways of expressing the interference factor,S(q), one of which was obtained by Sharan and others in the case of indium. By comparing these expressions with the latter, with those of corresponding cubic structures as well as with those obtained under spherical approximation respectively, the crystallographic equivalence and stability of tetragonal structures as well as the validity of Wigner-Seitz approximation are discussed.     

Distorted vortex lattice in a tetrahedral superconductor

The equilibrium shape and the orientation of the vortex lattice are studied for an s-wave tetrahedral superconductor in the vicinity of the upper critical field. The phase diagram, which includes transitions between rhombic and rectangular lattices, is constructed in the parameter space of the Ginzburg-Landau functional. The developed theory is applied to the heavy-fermion superconductor PrOs₄Sb₁₂. In a wide range of parameters, the shape of the vortex lattice is only weakly dependent on the temperature. The neutron scattering measurements of the vortex lattice in PrOs₄Sb₁₂ can be explained by particularities of the tetrahedral symmetry group and are further supported by analysis of the appropriate band structure calculations. The text was submitted by the authors in English.     

Isomer shift in binary iron alloys

The isomer shift of binary iron alloys is related to the itineracy of the valence electrons. The problem of a volume correction in disordered alloys is discussed and further avoided by using data of intermetallic compounds. From a large selection of possible parameters a linear combination of the electronegativityφ ^* and the electron densityn _ws in the Wigner-Seitz cell seems to be a good choice for fitting the data. The problem that these parameters are of minor importance for the cohesion in transition metal alloys is discussed.     

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

Motto:     

Global invariants and equilibrium states in lattice gases

It is now well known that, in addition to the physical conserved quantities, lattice gases also have other unphysical ones related to the discretization of their phase space. From an abstract point of view a lattice gas can be considered like a full discrete Markov processL and these spurious conserved quantities yield the existence of a nonspatially homogeneous equilibrium state forL ^k. We show that a particular set of these conserved quantities is of special interest: Its elements will be called regular. These regular invariants are simply built from the local ones and their projection on each node is always a locally conserved quantity. Moreover, for most models they are one-to-one related to the Gibbs states ofL ^k which remain factorized. It turns out that all the classical known spurious invariants are regular and one can exhibit simple conditions to build models with only regular invariants. For the latter it is then justified to determine the transport coefficients of the locally conserved densities with the Green-Kubo procedure.     

约化胞与电子衍射谱的标定

对应于14种布喇菲点阵有44种约化胞,不但约化矢的选法是唯一的,而且可以根据约化矢标量积矩阵(a·a b·b c·c b·c c·a a·b)的不同形式,确定布喇菲点阵类型。在晶体点阵已知的情况下,从点阵参数计算出倒易点阵中的平面约化胞,并与试验得到的电子衍射谱对比以标定衍射斑点的指数。在晶体点阵未知的情况下,从已知转角的两个电子衍射谱中选三个接近中心的衍射斑点,相当于三个低指数倒易矢量。由它们构成倒易点阵的一个初基胞,变换成正点阵的初基胞后,经过约化得出约化胞和相应的布喇菲单胞的类型和参数,同时标定衍射斑点的指数。这些标定计算已编成电子计算机程序,可以用来直接确定晶体点阵类型和进行物相分析。     

The Lattice and Simplex Structure of States on Pseudo Effect Algebras

We study states, measures, and signed measures on pseudo effect algebras with some version of the Riesz Decomposition Property (RDP). We show that the set of all Jordan signed measures is always an Abelian Dedekind complete ℓ-group. Therefore, the state space of a pseudo effect algebra with RDP is either empty or a nonempty Choquet simplex or even a Bauer simplex. This will allow to represent states on pseudo effect algebras by standard integrals.     

Internal space decimation for lattice gauge theories

By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed.     

Effects of Poisson's ratio on the band gaps and defect states in two-dimensional vacuum/solid porous phononic crystals

The effects of the Poisson’s ratio of the solid host on the band gaps and point defect states of the mixed elastic wave modes in two-dimensional vacuum/solid porous PNCs are studied by numerical simulations. Four typical systems are considered. The four systems are, respectively, (I) the system with a square lattice and circular pores, (II) the system with a hexagonal lattice and circular pores, (III) the system with a square lattice and square pores and (IV) the system with a hexagonal lattice and regular-hexagonal pores. In the latter two systems, with respect to the outer boundaries of the Wigner-Seitz unit cell, the pores rotate 45° and 30°, respectively. Some observable effects of the Poisson’s ratio are found in the numerical results. Especially, the variations of the band gap boundaries with the Poisson’s ratio exhibit relatively consistent behaviors. With the increase of the Poisson’s ratio, the normalized frequency of a band gap boundary generally increases, except that in system (III) the normalized frequency of the upper boundary of the first band gap remains almost unchanged. Detailed interpretations on this phenomenon are given.     

Perfect 3-dimensional lattice actions for 4-dimensional quantum field theories at finite temperature

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof.In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature-dependent coefficients. In this way the UV-problem and the infrared problem are separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations.In this paper we outline the principles for ϕ⁴-theory and scalar electrodynamics. The Bałaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here.     

Kinematics of multigrid Monte Carlo

We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonianþ(), the absence of critical slowing down can only be expected if the expansion of þ( +) in terms of the shift contains no relevant (mass) term. We also introduce a multigrid update procedure for non-abelian lattice gauge theory and study the acceptance rates for gauge groupSU(2) in four dimensions.     

基质发光材料Na5Eu(MoO4)4和NaEu(MoO4)2的喇曼光谱

本文研究了基质发光材料Na5Eu(MoO4)4和NaEu(MoO4)2的喇曼光谱.用群论方法分析了它们的内、外振动模式,对实验振动模进行了指认.本文还将上述喇曼光谱与Na5Eu(WO4)4、CaWO4、SrWO4、CaMoO4和SrMoO4的喇曼光谱进行了比较,Na5Eu(MoO4)4和NaEu(MoO4)2的喇曼光谱结果表明(MoO4)2-离子团的高能量拉伸内振动是产生Eu3+的5D2→5D1,5D1→5D0-多声子无辐射弛豫的原因,这导致了Eu3+在这类材料中主要产生5DO→7Fj的发光跃迁.     

Representation Theorem of Observables on a Quantum System

An orthomodular lattice (OML) with a conditional state can be used as a model for noncompatible events (a quantum system). In this paper we will study some properties of a conditional state and an s-map which are defined on an OML. We show conditions when a quantum system has the same properties as the classical probability space.     

Topological order in an exactly solvable 3D spin model

We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on Ω(R²) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.     

Quantum spin liquid on 2D rectangular frustrated AF lattice

The state of a 2D rectangular spin lattice with first, second and third nearest-neighbour anisotropic antiferromagnetic interactions is investigated. In a special line of parameter space, it is proved that the quantum spin liquid is the exact eigenstate of the system. For general parameter values, Green's function method with cut-off approximation is used to determine the phase diagram at zero temperature, and it is found that the quantum spin liquid appears on a rectangular lattice when the third nearest-neighbour interaction in the direction with shorter lattice spacing is introduced. The relations to the possibility of mixture of the spin liquid and the Fermi liquid in high-T _c superconductors are discussed.     

Existence of enantiomeric phase separation in a three-dimensional lattice gas model

A three-dimensional lattice gas model for enantiomeric phase separation is introduced. The enantiomeric molecules (d andl) are the two nonsuperimposable mirror images having the molecular structure C(AB)₂, where C is a tetrahedrally bonded carbon atom with one bond to each end of two AB groups. The lattice gas model consists of a body-centered cubic lattice, each site of which can be either vacant or occupied by a molecule oriented so that the A and B groups point toward neighboring lattice sites. Pairs of molecules interact with short-range, orientationally-dependent interactions. For a domain of interaction parameters, the Pirogov-Sinai extension of the Peierls argument is used to prove thatd-rich andl-rich phases exist in the model at sufficiently low temperature. For another domain of interaction parameters, at sufficiently high chemical potential there is an infinite number of ground states, each containing a racemic mixture ofd andl molecules.