Generalized transformation for decorated spin models

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising model. We apply this transformation to a particular mixed spin-(1/2, 1) and (1/2, 2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-S square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also includes combinations of three-body and four-body interactions; in particular we considered spin 1 and 2.     

A variational approach to distribution function theory

We present a novel formalism for the generation of integral equations for the distribution functions of fluids. It is based on a cumulant expansion for the free energy. Truncation of the expansion at theKth term and minimization of the resulting approximation leads to equations for the distribution functions up toKth order.The formalism is not limited to systems with two-body interactions and does not require the addition of closure relations to yield a complete set of equations. In fact, it automatically generates superposition approximations, such as the Kirkwood three-body superposition approximation or the Fisher-Kopeliovich four-body one.The conceptual approach is adapted from the cluster variation method of lattice theory.     

Modelling of a displacive transformation in two-dimensional system within a single-site approximation of continuous displacement cluster variation method

It is attempted to model a displacive phase transformation by Continuous Displacement Cluster Variation Method. The main focus of the present study is placed on distorted to non-distorted phase transformation in the two-dimensional square lattice. The entropy is formulated within the single-site approximation (point approximation), while the pair-wise atomic interaction energies are combined to stabilize a distorted phase at low temperatures. The distorted to non-distorted phase transformation in the present study is of the second order, and the calculated distribution of atoms suggests that the transformation is of the displacive type in the classification.     

Transformation optics for efficient calculation of transmembrane voltage induced on cells

We present a novel efficient approach in calculating induced transmembrane voltage(ITV) on cells based on transformation optics. As cell membrane is much thinner than the dimension of a typical cell, discretizing the membrane needs numerous meshes. Using an anisotropic medium based on transformation optics, the thickness of the membrane can be exaggerated by at least one order, which eliminates rigorous mesh refinement and reduces unknowns greatly. The accuracy and efficiency of the proposed method are verified by a cylindrical cell model. Moreover, the influence on ITV with bound water(BW) layers is also studied. The results show that when cells are exposed to nanosecond electric field, BW layers should be rigorously considered in calculating ITV.     

Four-Boson Systems Close to a Universal Regime

Universal properties of weakly-bound four-boson systems near the scaling limit are discussed by considering recent results obtained from the solution of Faddeev-Yakubovsky (FY) equations, which confirm a previous conjecture on a four-body scale dependence. In the present contribution, within a discussion on our numerical results obtained for the binding energies of two consecutive tetramer states, we are analyzing the relative relevance of the two possible configurations of the four-body system.     

Microscopic spin-wave theory for yttrium-iron garnet films

Motivated by recent experiments on thin films of the ferromagnetic insulator yttrium-iron garnet (YIG), we have developed an efficient microscopic approach to calculate the spin-wave spectra of these systems. We model the experimentally relevant magnon band of YIG using an effective quantum Heisenberg model on a cubic lattice with ferromagnetic nearest neighbour exchange and long-range dipole-dipole interactions. After a bosonization of the spin degrees of freedom via a Holstein-Primakoff transformation and a truncation at quadratic order in the bosons, we obtain the spin-wave spectra for experimentally relevant parameters without further approximation by numerical diagonalization, using efficient Ewald summation techniques to carry out the dipolar sums. We compare our numerical results with two different analytic approximations and with predictions based on the phenomenological Landau-Lifshitz equation.     

The integral equation approach to four-nucleon bound states

Within the framework of the Yakubovsky four-body equations the 0⁺ bound states of ⁴He are determined. The two-particle interactions used are of the separable Yamaguchi type and include spin-dependent forces. The problem is reduced to the solution of four coupled integral equations in two variables. The separable approximation of the kernels makes it possible to reduce the problem to a set of single variable integral equations. The separable approximation method employed is based on the Hilbert-Schmidt expansion applied to the kernels of four-body equations. The ground state energy of ⁴He is found to be ?45.73 MeV, the excited 0⁺ level lies at ?11.69 MeV. In conclusion we discuss the accuracy of various approximate methods in the four-nucleon problem.     

Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

We study a class of two-dimensional spin-1/2 Heisenberg antiferromagnets, introduced by Klein [1], in which the nearest-neighbor term is supplemented by next-nearest-neighbor pair and four-body interactions, producing additional frustration. For certain lattices, including e.g. the hexagonal lattice, we prove that any finite subset which admits a dimer covering has a ground state space spanned by valence bond states, each of which consists only of nearest-neighbor (dimer) singlet pairs. We also establish linear independence of these valence bond states. The possible relevance to resonating-valence-bond theories of high-temperature superconductors is briefly discussed. In particular, our results apply both to regular subsets of the lattice and to subsets with static holes.Work supported in part by N.S.F. Postdoctoral Research FellowshipsWork supported by N.S.F. Grant No. DMR-83-18051     

Plane-wave pseudopotential study for the structural stability of Hf: The role of spin-orbit interaction

With the use of density functional theory, first-principles calculation has been performed to investigate the structural stability of Hf. In this context, Hf has several characteristics, including the openness of its omega structure in the sequence hcp→omega→bcc with elevated pressure, its tight-binding d-bands near the Fermi level and the possible requirement of relativistic correction (spin-orbit coupling, SO) for its relatively high atomic number. To decouple these characters and reproduce the equilibrium transformation pressures of hcp→omega as well as omega→bcc, we treat Hf with (I) local density approximation (LDA) without and (II) with SO coupling, (III) generalized gradient approximation (GGA) without and (IV) with SO coupling. Our plane-wave pseudopotential calculation with GGA and SO interaction results in transformation pressures much closer to the experiment compared to the previous linear muffin-tin orbit calculations. Furthermore, we discuss the dependence of lattice parameters and the transformation pressure on SO coupling. The effect of SO on the correlation of d-band occupancy and the structural stability is also revealed.     

Four-Body Bound-States Systems in Relativistic Scalar Quantum Field Theory: Variational Basis-State Approach

The variational method within the Hamiltonian formalism of quantum field theory has been used in order to investigate the effect of virtual pairs for four-body scalar systems consisting of two particles and two antiparticles of the same mass. The scalar particles and antiparticles interact via a massive or massless mediating scalar field. The ground state energy solutions of Fock-space variational trial states (\(|N{\bar {N}}N{\bar {N}}{ \rangle }+|N{\bar {N}}N{\bar {N}}N{\bar {N}\rangle }\)) of the relativistic wave equations have been studied. We have compared these results with the previous work of four-body system (variational trial states of the form \(|N{ \bar {N}}N{\bar {N}}{\rangle }\)) and we have shown that the inclusion of virtual pairs has a noticeable effect at low coupling and at high coupling the energy of the system is changed by an important amount. In other words, the calculations show that the inclusion of virtual pairs augments the binding energy of the four-body system by a substantial amount at strong coupling. This study can pave the way for some new ideas in order to investigate the effect of virtual pairs, for example, for a bound-states quark-antiquark or tetraquark systems in future.     

Rearrangement Collisions between Four Identical Particles as a Four-Body Problem

Nuclear reactions between composite particles with rearrangement processes are considered. The cluster model is used in describing the structure of the nuclei. With this structure we have in the initial channel as well as in the final channel, four interacting particles. These reactions are studied as a four-body problem. The scattering amplitudes are approximated by using a separable expansion for the separable potential model. The four-body equations are reduced to integral equations in the form of exact effective two-particle Lippmann-Schwinger equations. These equations are solved by standard methods in a form suitable for numerical calculations. The present four-body treatment is applied calculating the differential cross-sections for different scattering and transfer nuclear reactions. Distorted wave Born approximation calculations are used in calculating the angular distributions. The present theoretical calculations are in good agreement with the experimental angular distributions.     

The computer simulation and classical interpretation of fast ion emission profiles near planes

Abstract

The techniques of computer simulation are used to generate the velocity distribution of ions emerging near close packed planes from a crystal surface. We concern ourselves in particular with protons and α-particles, 5 to 100 keV, near (100) planes in copper. The ions are initially emitted from either a lattice site-the ‘blocking case ‘or any other given point within a unit cell’ intermediate emission’. The resultant profiles are compared with an analytic model due to Andersen⁽⁶⁾ based on the continuum approximation, and the validity of this model is thereby assessed. A simpler analytic model in which the interplanar continuum potential is approximated by a pure harmonic is also developed and compared with the previous two. Using the harmonic approximation we obtain a relatively simple relationship between the yield measured exactly parallel to a plane and the position of the original emission site. It is suggested that such a relationship could be of importance for experiments that can measure nuclear lifetimes of the order of 10^?18 to 10^?16 seconds.     

Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.     

固氪物态方程的关联量子化学计算

运用多体展开理论和量子化学方法—–超分子单、双(三重)激发微扰处理耦合簇CCSD(T)方法,首次系统地计算了面心立方固氪在较宽(从晶格平衡位置到体积压缩率超过3倍)区间的两体、三体和四体相互作用对结合能和物态方程的贡献大小,包括Hartree-Fock自洽场项和范德瓦耳斯长程关联作用项;并与实验数据进行比较.结果表明,在考虑到两体、三体、四体相互作用能后,多体展开理论以及CCSD(T)方法对平衡位置结合能测量数据0—130 GPa整个研究区间的实验物态方程数据都做出令人满意的描述.     

Lattice dynamics and electron-phonon interaction in (3,3) carbon nanotubes

We present a detailed study of the lattice dynamics and electron-phonon coupling for a (3,3) carbon nanotube which belongs to the class of small diameter based nanotubes which have recently been claimed to be superconducting. We treat the electronic and phononic degrees of freedom completely by modern ab initio methods without involving approximations beyond the local density approximation. Using density functional perturbation theory we find a mean-field Peierls transition temperature of approximately 240 K which is an order of magnitude larger than the calculated superconducting transition temperature. Thus in (3,3) tubes the Peierls transition might compete with superconductivity. The Peierls instability is related to the special 2k(F) nesting feature of the Fermi surface. Because of the special topology of the (n,n) tubes we also find a phonon softening at the Gamma point.     

VARIATIONAL ANALYSIS OF CUMULANT EXPANSION IN SU(2) LATTICE GAUGE THEORY WITH AN ACTION INCLUDING SIX-LINK LOOPS

By using the cumulant expansion variational method,we study the SU(2) lattice action including six-link loops which satify the request of Symanzik.The average values of the plaquette and six-link loop up to second order approximation are calculated.Our results are consistant with Monte Carlo data.     

Spin compensation temperatures in the mean-field approximation of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system

The magnetic behaviors of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system on a square lattice are studied with the mean-field approximation (MFA) based on the Bogoliubov inequality for the free energy. A Landau expansion of the free energy in the order parameter is also described in this work. In particular, we investigate the effect of a single-ion anisotropy on the compensation phenomenon.     

The lattice baryon spectrum in first order strong coupling approximation

Lattice baryon masses are calculated in first order strong coupling approximation with staggered fermions. Particular emphasis is given to the lattice quantum numbers and their relation to the continuum symmetry. Using non-local one-link fields, we found lattice baryon states which are new in first order strong coupling approximation.     

First principles study of structural and electronic properties of different phases of boron nitride

A theoretical study of structural and electronic properties of the four phases of BN (zincblende, wurtzite, hexagonal and rhombohedral) is presented. The calculations are done by full potential (linear) augmented plane wave plus local orbitals (APW+lo) method based on the density functional theory (DFT) as employed in WIEN2k code. Using the local density approximation (LDA) and generalized gradient approximation (GGA-PBE) for the exchange correlation energy functional, we have calculated lattice parameters, bulk modulus, its pressure derivative and cohesive energy. In order to calculate electronic band structure, another form of the generalized gradient approximation proposed by Engel and Vosko (GGA-EV) has been employed along with LDA and GGA-PBE. It is found that all the three approximations exhibit similar band structure qualitatively. However, GGA-EV gives energy band gap values closer to the measured data. Our results for structural and electronic properties are compared with the experimental and other theoretical results wherever these are available.