An−1(1) reflection K-matrices

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the A_n−1⁽¹⁾ affine Lie algebra. We have classified them in two classes of solutions. The first class consists of n(n−1)/2 K-matrix solutions with three free parameters. The second class are solutions that depend on the parity of n. For n odd there exist n reflection K-matrices with 2+[n/2] free parameters. It turns out that for n even there exist n/2 K-matrices with 2+n/2 free parameters and n/2 K-matrices with 1+n/2 free parameters.     

Bethe ansatz solution for quantum spin-1 chains with boundary terms

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov–Fateev and Izergin–Korepin, and the Z₂-graded 19-vertex models with sl(2|1) and osp(1|2) invariances. In each case the eigenspectrum is determined by application of the coordinate Bethe ansatz.     

Integrable supersymmetric correlated electron chain with open boundaries

We construct an extended Hubbard model with open boundaries from an R-matrix based on the U_q[Osp(2|2)] superalgebra. We study the reflection equation and find two classes of diagonal solutions. The corresponding one-dimensional open Hamiltonians are diagonalized by means of the Bethe ansatz approach.     

On a2(1) reflection matrices and affine Toda theories

We construct new non-diagonal solutions to the boundary Yang-Baxter equation corresponding to a two-dimensional field theory with U_q(a₂⁽¹⁾) quantum affine symmetry on a half-line. The requirements of boundary unitarity and boundary crossing symmetry are then used to find overall scalar factors which lead to consistent reflection matrices. Using the boundary bootstrap equations we also compute the reflection factors for scalar bound states (breathers). These breathers are expected to be identified with the fundamental quantum particles in a₂⁽¹⁾ affine Toda field theory and we therefore obtain a conjecture for the affine Toda reflection factors. We compare these factors with known classical results and discuss their duality properties and their connections with particular boundary conditions.     

Integrability of a family of quantum field theories related to sigma models

A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2|1) Toda theory, and the N=2 supersymmetric sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS₂×S², and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space.     

Elliptic three-boson system, “two-level three-mode” JCD-type models and non-skew-symmetric classical r-matrices

Using the technique of the classical r-matrices and quantum Lax operators we construct the most general form of quantum integrable multi-boson and spin-multi-boson models associated with linear Lax algebras and sl(2)⊗sl(2)-valued classical non-dynamical r-matrices with spectral parameters. We consider example of non-skew-symmetric elliptic r-matrix and explicitly obtain one-, two- and three-boson integrable models and the corresponding one-, two- and three-mode two-level Jaynes-Cummings-Dicke-type models. We show that integrable “elliptic” two-level one-mode Jaynes-Cummings-Dicke Hamiltonian is hermitian and contains both rotating and counter-rotating terms.     

Dn+1(2) reflection K-matrices

We investigate the possible regular solutions of the boundary Yang–Baxter equation for the vertex models associated with the D_n+1⁽²⁾ affine Lie algebra. We have classified them in terms of three types of K-matrices. The first one has n+2 free parameters and all the matrix elements are non-zero. The second solution is given by a block diagonal matrix with just one free parameter. It turns out that for n even there exists a third class of K-matrices without any free parameter.     

Chemical shift of the Ga and As Kα1,2 and Kβ1,3 X-ray emission lines

By means of a double crystal spectrometer and a computer the chemical shifts of the Ga Kα_1,2, As Kα_1,2 and Kβ_1,3 lines were determined with high accuracy. An interpretation of the results obtained with a free ion model and a calculation according to the Hartree method shows agreement of the values calculated for the effective atomic charges with those based on chemical experience, and also the presence of a charge transfer from the A atom to the B atom in A^IIIB^V compounds. The existence of binding charges is one of the reasons for the fact that |q_A| ≠ |q_B|. The interpretation of the Kβ_1,3 and Lα shifts shows the limitations of the free ion model.     

The chiral-bag model andK→2π decays

Nonleptonic kaon decays (K→2π) have been analyzed using the chrial-bag model. This continues the research of nonleptonic decays by the authors (Ref. [7] below). The results obtained are in qualitative agreement with those based on QCD-duality. the decay amplitudeA(K ⁺→π⁺π⁰) (ΔI=3/2) can be explained while the ΔI=1/2 decay amplitudes are 4 to 5 times smaller then the observed values. The ratio ofK ⁰ decay amplitudes ξ=|A(K ⁰→π⁺π^?)/A(K ⁰→π⁰π⁰| is larger than one, as it is experimentally. This is an improvement in comparison with MIT-bag model, where ζ was always smaller than one, even if ΔI=1/2 pieces in the theoretical expressions were enhanced.     

Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices

The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of two- and three-state vertex models. These models include the six-vertex model, the 15-vertex A₂⁽¹⁾ model and the 19-vertex models of Izergin-Korepin and Zamolodchikov-Fateev. In each case the eigenspectra is determined by application of either the algebraic or the analytic Bethe ansatz with inhomogeneities. With suitable choices of reflection matrices, these vertex models can be associated with integrable loop models on the same lattice. In general, the required choices do not coincide with those which lead to quantum-group-invariant spin chains. The exact solution of the integrable loop models — including an O(n) model on the square lattice with open boundaries — is of relevance to the surface critical behaviour of two-dimensional polymers.     

Resonance production in the reaction π±p→Ks0K±p at 30 and 50 GeV/c

The mass and momentum transfer spectra of the charged $\text{K}\text{K}$ system produced in the reaction π^±p→K_s⁰K^±p are analyzed. The data have been collected at the CERN SPS with the Geneva-Lausanne two-arm, non-magnetic spectrometer at 30 and 50 GeV/c incident momenta. The general features of the reactions at these energies and the results of partial-wave analyses of the two kaon system are presented.The channel is dominated by the diffractive production of even spin resonances. The spin 4 recurrence of the A₂(1320) is clearly observed at 2040 MeV (Γ=380 MeV. A new resonance is observed with a mass M=2450MeV and a width Γ=400 MeV; the quantum numbers of this state are found to be I^G(J^PC)=1^?(6++). The analysis also shows the decay of the decay of the meson ?′(1600) through the $\text{K}\text{K}$ channel at both energies.The production amplitudes are determined both as a function of the $\text{K}\text{K}$ effective mass and of the momentum transfer. Isoscalar natural parity exchange is dominant. The energy dependence between 10 and 50 GeV/c is shown to be well described by a Regge pole model based on the f-dominated pomeron hypothesis. We compare the production mechanisms of the 2⁺ resonances A₂(1320) and K¹(1430). Finally, we estimate the $\text{K}\text{K}$ branching ratios of the spin 4 A₂(2040) and spin 6 A₂(2450) resonances.     

Quantum affine algebras and universalR-matrix with spectral parameter

Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U _q (A ₁ ⁽¹⁾ ) and U _q (A ₂ ⁽¹⁾ ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U _q (A ₁) and U _q (A ₂). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U _q (A ₂), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.     

sl(2) variational schemes for solving one class of nonlinear quantum models

Hamiltonians of a wide-spread class of G_inv invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as nonlinear functions of sl(2) generators. This enables us to use variational schemes, based on sl(2) generalized coherent states as trial functions, to obtain new (sl(2) cluster) quasi-classical solutions of spectral and evolution tasks which smoothly approximate exact ones and catch explicitly quantum cooperative features of the models under study (in contrast with standard independent-mode quasi-classical approximations). In such a way new analytical expressions are found for the energy spectra which are beyond both equidistant and quasi-equidistant ones obtained earlier.     

Algebraic construction of higher-rank dilute A models

Starting from representations of the Birman-Wenzl-Murakami algebra underlying the critical B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾ RSOS models of Jimbo, Miwa and Okado, we derive four series of solvable, critical RSOS models associated with the twisted affine Lie algebra A_n⁽²⁾. Two of these are the critical limit of the A_2n−1⁽²⁾ and A_2n⁽²⁾ models obtained previously by Kuniba. The other two series, again one of the A_2n−1⁽²⁾ and one of the A_2n⁽²⁾ type, are new, and the latter generalizes the dilute A models to arbitrary rank n. For the two new series we present an elliptic extension which satisfies the Yang-Baxter equation, and show that for certain values of the parameters the higher-rank dilute A models break the ℤ₂ symmetry of the underlying adjacency graphG, whereGis the level-l C_n⁽¹⁾ weight lattice.     

Studies of interface phonons

The vibrational modes localized at the interface between two distinct crystals have been studied for a simple crystal model obeying all of the invariance conditions required for models used in studies of dynamical properties of crystal surfaces, and giving rise to Rayleigh surface waves. The two crystals are assumed to be semi-infinite simple cubic and to have the same lattice parameter a. They differ by their mass (M and M_A) and the central force interactions between first (K and K_a) and second nearest neighbors $\text{1}\text{2}\text{K}$ and $\text{1}\text{2}\text{K}{}_{\mathrm{A}}$. The interface is obtained by coupling the (001) free surfaces of these distinct crystals by central force intractions (K^'). We find that the variation of the interaction conditions (K^') at the interface and of the $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{A}}\text{M}{}_{\mathrm{A}}\text{)}$ parameter has the following qualitative effects on the properties of surface and bulk phonons. When (K^') increases from zero to a finite value, the frequencies of the surface phonons increase and are splitted in the case of two identical crystals. One can say that the surface phonons are transformed into interface modes. For some values of $\text{K}{}^{\mathrm{\text{'}}}\text{K}$ and $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{<mtext>A</mtext>}}\text{M}{}_{\mathrm{<mtext>A</mtext>}}\text{)}$ parameters these interface phonons may be admixed with bulk phonons and thus become virtual interface states.     

Construction of tensor exchange amplitudes in KN and KN CEX reactions

K⁺n charge exchange (CEX) polarization data obtained recently by the Saclay group at CERN are supplemented by differential cross-section data and by information on K^?p CEX, and used to construct tensor exchange non-flip and flip components T₀ and T₁ of the s-channel helicity amplitudes directly from data at 6 GeV/c and for |t| ? 0.9. Vector exchange amplitudes are assumed to be known from πN scattering. The sensitivity of solutions to the uncertainties in the input data is examined in great detail. In general we find a unique solution for all t.We observe new features in the t-structure of non-flip and flip amplitudes. Re T₀Re T₀ have simple zeros at t ≈ ?0.45 and t ≈ ?0.65. Im T₀ has a dip or a double zero at t ≈ ?0.16 and a double zero structure at t ≈ ?0.45. Im T₁ has two simple zeros at t ≈ ?0.45 and t ≈ ?0.70. Violations of weak EXD in both amplitudes correspond to a lower A₂ trajectory by approximately Δα ≈ 0.1. If certain conditions are satisfied by the input data, a discrete ambiguity exists in the solutions for |t| ? 0.55 and this possibility is also carefully examined.     

Anharmonic oscillator model for first order structural phase transition

Exact solutions for the motion of a classical anharmonic oscillator in the potentialV(φ)=Bφ ² ? |A|φ ⁴ +Cφ ⁶ are obtained in (1 + 1) dimensions. Instanton-like solutions in (imaginary time) which takes the particle from one maximum of the potential to the other are obtained in addition to the usual oscillatory solutions. The energy dependence of the frequencies of oscillation is discussed in detail. This can be used as a model for the first order structural phase transition in the mean field approximation. The high and low temperature behaviour of the static susceptibility is obtained. Finally, a qualitative explanation is offered for the observed central peak in ferroelectrics like SrTiO₂.     

TheA n /(1) face models

Presented here is the construction of solvable two-dimensional lattice models associated with the affine Lie algebraA _n ^/(1) and an arbitrary pair of Young diagrams. The models comprise two kinds of fluctuation variables; one lives on the sites and takes on dominant integral weights of a fixed level, the other lives on edges and assumes the weights of the representations ofsl(n+1, C) specified by Young diagrams. The Boltzmann weights are elliptic solutions of the Yang-Baxter equation. Some conjectures on the one point functions are put forth.