We investigate the algebraic structure of the supersymmetric t-J model in one dimension. We prove that the Bethe ansatz states are highest-weight vectors of an spl(2,1) superalgebra. By acting with shift operators we construct a complete set of states for this model. In addition we analyse the multiplet Structure of the anti-ferromagnetic ground state and some low-lying excitations. It turns out that the ground state is a member of a quartet.

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In this work we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunneling. Using direct numerical diagonalisation of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalised and self-trapping phases. We show that these behaviours are dependent on both the initial state of the system as well as regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.

A general form factor formula for the scaling Z(N )-Ising model is constructed. Exact expressions of all matrix elements are obtained for several local operators. In addition, the commutation rules for order, disorder parameters and para-Fermi fields are derived. Because of the unusual statistics of the fields, the quantum field theory seems to be not related to any classical Lagrangian or field equation.

The form factor equations are solved for a SU (N) invariant S-matrix under the assumption that the anti-particle is identified with the bound state of N − 1 particles. The solution is obtained explicitly in terms of the nested off-shell Bethe ansatz where the contribution from each level is written in terms of multiple contour integrals. The general solution is illustrated for some operators, such as the energy-momentum tensor, the fields and the current.

Abstract. The purpose of the "bootstrap program" for integrable quantum field theories in 1+1 dimensions is to construct explicitly a model in terms of its Wightman functions. In this article, this program is mainly illustrated in terms of the sinh-Gordon model and the SU (N ) Gross-Neveu model. The nested off-shell Bethe ansatz for an SU (N ) factorizing S-matrix is constructed. We review some previous results on sinh-Gordon form factors and the quantum operator field equation. The problem of how to sum over intermediate states is considered in the short distance limit of the two point Wightman function for the sinh-Gordon model.

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds.Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP) 2 CuBr 4 ·2H 2 O, Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 etc.