Interfacial behavior of tetrapyridylporphyrin monolayer arrays

The behavior of monolayer films of free base 5,10,15,20-tetrapyridylporphinato (TPyP) and 5,10,15,20-tetrapyridylporphinato zinc(II) (ZnTPyP) on pure water, 0.1 M CdCl2, and 0.1 M CuCl2 subphases was investigated by surface pressure-area isotherms, specular X-ray reflectometry, and polarized total reflection X-ray absorption spectroscopy (PTRXAS). Surface pressure-area isotherms showed significant differences in the area per molecule on pure water compared to that on salt subphases, with a marked increase in the area observed on the salt solutions. This behavior was noted for both forms of the porphyrin and both salts investigated. Modeling of specular X-ray reflectometry data indicated that thinner and more electron dense layers on salt subphases best fit the observed profiles. These data suggest that the porphyrin macrocycle is oriented parallel to the interface on salt subphases and takes on a tilted conformation on pure water. In the case of ZnTPyP, PTRXAS was used to determine the orientation of the porphyrin moiety relative to the surface and to probe the coordination of the central Zn ion. In agreement with the pressure-area isotherms and reflectometry, the PTRXAS data indicate a change in orientation on the salt subphases.

On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras

The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U-q (gl(m/n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U-q[osp(m/n)]. In this manner, we obtain generalizations of the Perk-Schultz model.