C. Zambon

CLASSICALLY INTEGRABLE FIELD THEORIES WITH DEFECTS

Some ideas and remarks are presented concerning a possible Lagrangian approach to the study of internal boundary conditions relating integrable fields at the junction of two domains. The main example given in the article concerns single real scalar fields in each domain and it is found that these may be free, of Liouville type, or of sinh-Gordon type.

Affine Toda field theories with defects

A lagrangian approach is proposed and developed to study defects within affine Toda field theories. In particular, a suitable Lax pair is constructed together with examples of conserved charges. It is found that only those models based on ar(1) data appear to allow defects preserving integrability. Surprisingly, despite the explicit breaking of Lorentz and translation invariance, modified forms of both energy and momentum are conserved. Some, but apparently not all, of the higher spin conserved charges are also preserved after the addition of contributions from the defect. This fact is illustrated by noting how defects may preserve a modified form of just one of the spin 2 or spin -2 charges but not both of them.

Some aspects of jump-defects in the quantum sine-Gordon model

The classical sine-Gordon model permits integrable discontinuities, or jump-defects, where the conditions relating the fields on either side of a defect are Backlund transformations frozen at the defect location. The purpose of this article is to explore the extent to which this idea may be extended to the quantum sine-Gordon model and how the striking features of the classical model may translate to the quantum version. Assuming a positive defect parameter there are two types of defect. One type, carrying even charge, is stable, but the other type, carrying odd charge, is unstable and may be considered as a resonant bound state of a soliton and a stable defect. The scattering of solitons with defects is considered in detail, as is the scattering of breathers, and in all cases the jump-defect is purely transmitting. One surprising discovery concerns the lightest breather. Its transmission factor is independent of the bulk coupling — a property susceptible to a perturbative check, but not shared with any of the other breathers. It is argued that classical jump-defects can move and some comments are made concerning their quantum scattering matrix.

On purely transmitting defects in affine Toda field theory

Affine Toda field theories with a purely transmitting integrable defect are considered and the model based on a2 is analysed in detail. After providing a complete characterization of the problem in a classical framework, a suitable quantum transmission matrix, able to describe the interaction between an integrable defect and solitons, is found. Two independent paths are taken to reach the result. One is an investigation of the triangle equations using the S-matrix for the imaginary coupling bulk affine Toda field theories proposed by Hollowood, and the other uses a functional integral approach together with a bootstrap procedure. Evidence to support the results is collected in various ways: for instance, through the calculation of the transmission factors for the lightest breathers. While previous discoveries within the sine-Gordon model motivated this study, there are several new phenomena displayed in the a2 model including intriguing disparities between the classical and the quantum pictures. For example, in the quantum framework, for a specific range of the coupling constant that excludes a neighbourhood of the classical limit, there is an unstable bound state.

A transmission matrix for a fused pair of integrable defects in the sine-Gordon model

Within the quantum sine-Gordon model a transmission matrix describing the scattering of a soliton with a fused pair of integrable defects is proposed. The result is consistent with the classical picture of scattering and highlights the differences between two defects located at separated points and two defects fused at the same point. Moreover, the analysis reveals how, for certain choices of parameters, both the soliton–soliton and the lightest breather–soliton S-matrices of the sine-Gordon model are embedded within the transmission matrix, supporting an interpretation in which defects may be regarded as soliton constituents.

Comments on defects in the ar Toda field theories

A simple, basic argument is given, based solely on energy–momentum considerations, to recover conditions under which ar affine or conformal Toda field theories can support defects of integrable type. Associated triangle relations are solved to provide expressions for transmission matrices that generalize previously known examples calculated for the sine-Gordon model and the a2 affine Toda model.

Integrable defects in affine Toda field theory and infinite-dimensional representations of quantum groups

Abstract Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang–Baxter equations, and second by solving a linear intertwining relation between a finite-dimensional representation of the relevant Borel subalgebra of the quantum group underpinning the integrable quantum field theory and a particular infinite-dimensional representation expressed in terms of sets of generalised ‘quantum’ annihilation and creation operators. The principal examples analysed are based on the a 2 ( 2 ) and a n ( 1 ) affine Toda models but examples of similar infinite-dimensional representations for quantum Borel algebras for all other affine Toda theories are also provided.

The classical nonlinear Schrodinger model with a new integrable boundary

A bstractA new integrable boundary for the classical nonlinear Schrödinger model is derived by dressing a boundary with a defect. A complete investigation of the integrability of the new boundary is carried out in the sense that the boundary K

Crystallographic stacking faults in antiferromagnetically coupled media

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