Narrow Results

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Bäcklund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical r-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.

We analyze some aspects of the kinematic theory of non-uniformly defective elastic crystals. Concentrating on the problem of identifying continuous defective lattices possessing the given defectiveness, as defined by the dislocation density tensor, we investigate the relation between the dislocation density tensor and the Lie algebra of vector fields associated with a defective lattice.

In this paper, we discuss a new way to get a quantum holonomy around topological defects in $C_{60}$ fullerenes. For this, we use a Kaluza–Klein extra dimension approach. Furthermore, we discuss how an extra dimension could promote the formation of new freedom degrees which would open a discussion about a possible qubits computation.