Exact form factors in (1 + 1)-dimensional field theoretic models with soliton behaviour

A system of equations is derived which must be satisfied by multiparticle matrix elements of any local operator in field theories with soliton behaviour. Form factors of various operators of interest are calculated exactly by means of the known exact S-matrices in the sine-Gordon, massive Thirring, non-linear σ^?, and Gross-Neveu models. The finite sine-Gordon wave function renormalization constant is determined exactly.     

Solution of then-channel Kondo problem (scaling and integrability)

The exact solution of the Kondo model forn-flavours of electrons with the spin 1/2 scattered by theS-spin impurity is presented. Forn=2S=5 the model describes manganese impurities dissolved in a metal. It is shown that atn>2S the effective exchange coupling approaches a finite fixed point as the energy scale decreases. It means that atn>2S the Gell-Mann-Low function turns to zero in this point and the scaling behaviour of physical quantities is observed. The scaling behaviour, first obtained in the 1D quantum field theory, can be analyzed on the basis of the exact solution. In the casen≦2S the effective coupling becomes infinitely strong at low energies.     

A set of exactly solvable Ising models with half-odd-integer spin

We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the free fermion condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S is given by S+1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.     

Modal series solution for an epidemic model

In this article, we generalize a recently proposed method to obtain an exact general solution for the classical Susceptible, Infected, Recovered and Susceptible (SIRS) epidemic mathematical model. This generalization is based upon the nonlinear coupling of two frequencies in an infinite modal series solution. It is shown that these series provide a nonstandard approach in order to obtain an accurate analytical solution for the classical SIRS epidemic model. Numerical results of the SIRS epidemic model for real and complex frequencies are included in order to test the validity and reliability of the method. This method could be applied to a wide class of models in physics, chemistry or engineering.     

Dynamical Arrest,Tracer Diffusion and Kinetically Constrained Lattice Gases

We analyze the tagged particle diffusion for kinetically constrained models for glassy systems. We present a method, focusing on the Kob–Andersen model as an example, which allows to prove lower and upper bounds for the self-diffusion coefficient D _S. This method leads to the exact density dependence of D _S, at high density, for models with finite defects and to prove diffusivity, D _S > 0, at any finite density for highly cooperative models. A more general outcome is that under very general assumptions one can exclude that a dynamical transition, like the one predicted by the Mode-Coupling-Theory of glasses, takes place at a finite temperature/chemical potential for systems of interacting particle on a lattice.     

The exact solution of 2D ZN invariant statistical models

The exact solution of the hamiltonian version of Z_N invariant statistical models at τ ≠ 0 is found by means of the Bethe-ansatz technique.     

Spin diffusion in anisotropic Heisenberg chains: S≥1/2

In this paper, we investigate spin diffusion in Heisenberg chains with uniaxial nearest-neighbor interactions. The approach followed is based on an analysis of the infinite-temperature longitudinal spin density and spin current correlation functions. For S=1/2, exact results are presented for the time-dependent correlation functions in the XY limit. Away from this limit, the second and fourth moments of the Fourier transform of the spin density correlation function provide information about spin dynamics for arbitrary values of the spin. The moments are used in an assessment of the accuracy of the Gaussian approximation for the spin diffusion constant for S=1/2. The general behavior of the Gaussian approximation when S>1/2 is discussed, and numerical results for the spin diffusion constant are presented for S=1/2, 1, 3/2, 2 and in the classical limit. A moment-based criterion for the boundary in reciprocal space between diffusive and non-diffusive dynamics that applies to arbitrary values of the spin is presented.     

Deformations of Fermionic Quantum Field Theories and Integrable Models

Considering the model of a scalar massive Fermion, it is shown that by means of deformation techniques it is possible to obtain all integrable quantum field theoretic models on two-dimensional Minkowski space which have factorizing S-matrices corresponding to two-particle scattering functions S ₂ satisfying S ₂(0) = ?1. Among these models there is for example the Sinh-Gordon model. Our analysis provides a complement to recent developments regarding deformations of quantum field theories. The deformed model is investigated also in higher dimensions. In particular, locality and covariance properties are analyzed.     

Non-integrable quantum field theories as perturbations of certain integrable models

We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and form factors of the integrable field theories we obtain the first-order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ T_c and the scaling region around the minimal model M_2,7. For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalisation of their Hamiltonian.     

Quantum S-matrix of the (1 + 1)-dimensional Todd chain

Exact factorized S-matrices are proposed for two models of (1 + 1)-dimensional quantum field theory: the Z(N) symmetric (1 + 1)-dimensional Todd chain and the e^? + e^?2? model.     

A novel Galerkin-like weakform and a superconvergent alpha finite element method (SαFEM) for mechanics problems using triangular meshes

A carefully designed procedure is presented to modify the piecewise constant strain field of linear triangular FEM models, and to reconstruct a strain field with an adjustable parameter α. A novel Galerkin-like weakform derived from the Hellinger–Reissner variational principle is proposed for establishing the discretized system equations. The new weak form is very simple, possesses the same good properties of the standard Galerkin weakform, and works particularly well for strain construction methods. A superconvergent alpha finite element method (SαFEM) is then formulated by using the constructed strain field and the Galerkin-like weakform for solid mechanics problems. The implementation of the SαFEM is straightforward and no additional parameters are used. We prove theoretically and show numerically that the SαFEM always achieves more accurate and higher convergence rate than the standard FEM of triangular elements (T3) and even more accurate than the four-node quadrilateral elements (Q4) when the same sets of nodes are used. The SαFEM can always produce both lower and upper bounds to the exact solution in the energy norm for all elasticity problems by properly choosing an α. In addition, a preferable-α approach has also been devised to produce very accurate solutions for both displacement and energy norms and a superconvergent rate in the energy error norm. Furthermore, a model-based selective scheme is proposed to formulate a combined SαFEM/NS-FEM model that handily overcomes the volumetric locking problems. Intensive numerical studies including singularity problems have been conducted to confirm the theory and properties of the SαFEM.     

Groundstate-calculation for the T-t Jahn-Teller system by an exponential transformation approach

The dynamical T-t Jahn-Teller problem is handled by a canonical exponential transformation exp (- S) H exp (S). The groundstate wavefunction of the diagonal part of H is given in the transformed and original space. Its expectation value for the total Hamiltonian is shown to agree with the exact numerical groundstate results up to intermediate coupling strengths. For strong coupling values the dominant k power still seems to be given correctly. However, in this limiting case exact results can be derived by a second transformation. Both types of transformations lead in a combined form to very accurate groundstate energies, which can be fitted with respect to the given numerical values.     

Critical exponents of S=1/2 Heisenberg ladders with ferromagnetic interchain interaction in magnetic fields

The critical properties of the S=1/2 Heisenberg two-leg ladders with a ferromagnetic interchain interaction in magnetic fields are investigated by combining the numerical exact diagonalization method and the finite-size-scaling analysis based on conformal field theory.     

Oscillator strengths for the 2s2, 2p2, 2s3s(1S)-2s2p(1P) transitions of B(II)

Accurate configuration interaction wavefunctions for the 2s²(¹S), 2p²(¹S), 2s3s(¹S) and 2s2p (¹P) states of B(II) are calculated in a single optimized orbital basis of 7s, 6p and 4d Slater-type orbitals. 95, 84, 57 and 90% of the correlation energies, respectively, are realized by these wavefunctions. Oscillator strengths for the three ¹S-¹P transitions are calculated from these and from less accurate wavefunctions in the same orbital basis. The length values obtained from our most accurate wavefunctions, in order of increasing ¹S energy, are 0.9885, 0.202 and 0.007. The degree of accuracy of these oscillator strengths is estimated by noting the convergence to final values as increasing percentages of correlation energies are included in the wavefunctions together with the increasing agreement between length and velocity formulas. The exact theoretical oscillator strength for the resonant line is projected to be 0.985 with an error almost certainly not greater than ±0.015. The theoretical oscillator strengths for the other lines are considered to be 0.21±0.02 and less than 0.007, respectively.     

X-ray and spectroscopic investigations on polycrystalline CoxZn1−xIn2S4 solid solution

The system Co_xZn_1?xIn₂S₄ is investigated by means of X-ray diffraction, optical and EFR spectra. The ZnIn₂S₄-type structure exists up to x = 0.60, and spectroscopic investigations suggest that the cobalt ions are distributed among the tetrahedral as well as octahedral sites of the lattice.     

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ _s in the ordered phase and the vortex-condensate stiffness ρ _v in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρ _s,v /Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ _s /ρ _v admits a quantitative measure of deviation from selfduality.     

The S-matrix of a factorizable supersymmetric Z(N) model

The exact S-matrix of a two-dimensional supersymmetric Z(N) model is computed. Antiparticles appeart as bound states of particles setting a rich spectrum structure.     

Inhomogeneous mixmaster universes: Some exact solutions

Algorithms for generating new exact solutions of the Einstein-Klein-Gordon field equations, which describe inhomogeneous universes with S³ topology of spatial sections, are developed. The known exact vacuum and stiff-fluid solutions with S³ topology are used as an input. The methods developed are further applied to derive inhomogenous generalizations of Bianchi type IX solutions and inhomogeneous S³ Gowdy models with gravitational and scalar waves. It is shown that the new solutions, which are generalizations of the Bianchi type IX models, permit identification of the scalar field with the velocity potential of the stiff irrotational fluid. The latter result is further used to study the growth rate of density perturbations of the isotropic and anisotropic Bianchi type IX universes in a fully nonlinear relativistic regime. The role of anisotropy of the rate of growth of density perturbations is studied in detail.