T-duality in Affine NA Toda Models

The construction of non-Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non-conformal two-dimensional integrable models naturally leads to the construction of a pair of actions, which share the same spectra and are related by canonical transformations.     

Binding of Ionic Pyrene Derivatives to Polyelectrolytes. A Uv Absorption and Fluorescence Study

Abstract

The binding of pyrenesulfonic acid and pyrenebutyric acid to poly(vinyl benzyl trimethylammonium) chloride was investigated by UV and fluorescence spectroscopy. It was found that the binding constant was 7.5 × 10⁴ and 3.5 × 10⁴M^?1, respectively. The addition of the polyelectrolyte quenches the fluorescence of the pyrene group, and at the same time the typical excimer emission appears. This emission originates in pre-formed ground state aggregates of the pyrene derivatives incorporated into the polyion domain. Similar effects were observed when anionic polyelectrolytes, poly(styrene sulfonic), and poly(vinyl sulfonic) acids were added to cationic pyrene derivatives. The binding constants depend on the length of the aliphatic sidechain of the derivatives.     

Integrable field theories with defects

The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the super sinh-Gordon model is constructed and shown to generate the Backlund transformations for its soliton solutions.     

Super-WZNW with reductions to supersymmetric and fermionic integrable models

A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to half integer graded affine Kac–Moody algebras. Explicit examples of the N=1,2 super-sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets sl(p,1)/sl(p)u(1) when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when p=2 leads to the constrained Bukhvostov–Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross–Neveu models.     

The 2-dimensionalN=2 supersymmetric Yang-Mills model on the discrete space-time lattice

We use the Dirac-Kähler formalism in order to put a two-dimensional Yang-Mills theory with a complex supersymmetry on the Euclidean space-time lattice. The theory presents two supersymmetric invariant actions related to each other by a kind of “time reflection” transformation.     

Phase transition in a generalized Dicke model of superradiance

By means of the use of the “gap equations”, we calculate the thermodynamic properties of a sufficiently general Dicke model. We obtain the general relations which correspond to the condition of second-order phase transition from the normal to the superradiant state.     

A FLUORESCENCE STUDY OF THE INTERACTION OF INDOLIC COMPOUNDS WITH SYNTHETIC POLYELECTROLYTES

Abstract— –The interaction of indole derivatives with synthetic polyelectrolytes was investigated using UV absorption and fluorescence spectroscopy. The presence of both sodium poly(styrene sulfonate) (PSS) and sodium polyvinyl sulfonate) (PVS) inhibits the fluorescence quenching of 1-pyrene sulfonic acid by tryptamine. The effect is more marked for PSS than for PVS. There was no polyelectrolyte effect on the quenching by tryptophan. It was also found that aromatic polyelectrolytes strongly quench the fluorescence of indole derivatives of opposite charge by a static mechanism. This is accompanied by a new absorption in the red extreme of the UV spectrum of the mixtures. The systems investigated were tryptamine-PSS and polyvinyl benzyl trimethylammonium chloride) with the anions of indole-3-alkanoic acids. Equilibrium constants for the binding of the indole derivatives to the polyelectrolytes were determined. The fluorescence of zwitterionic tryptophan is not affected by the presence of the polyelectrolytes.     

Riccati-Type Equations, Generalised WZNW Equations, and Multidimensional Toda Systems

We associate to an arbitrary ℤ-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer–Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given. Received: 3 August 1998 / Accepted: 21 December 1998