Aspects of Integrable Defects

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Defects and impurities are ubiquitous in nature and essential for the understanding of phenomena in many domains of physics ranging from classical continuum mechanics to condensed matter physics, or cosmology. In every case, a defect is likely to be modeled by a discontinuity in a field variable, such as the abrupt change in fluid velocity across a shock, or the discontinuity in the derivative of a wave function in the presence of an impurity. From a mathematical point of view it is natural to ask what kinds of defect can be supported by an integrable field theory without destroying integrability. Some integrable models do appear to be useful in certain special physical situations but it remains to be seen if the defects they can support are themselves relevant. The purpose of this talk is exploratory, to discover what might be possible and review a collection of ideas and questions. The main points to be addressed are: examples of integrable defects and the special role played by energy-momentum conservation and B\"acklund transformations; the description of solitons scattering with defects and some curious unanticipated effects;
the description of defects in integrable quantum field theory and associated transmission matrices; integrable field theories with boundaries revisited.
Original languageEnglish
Title of host publicationProceedings of the XXIX International Colloquium on Group Theoretical Mthods in Physics
Subtitle of host publicationSymmetries and Groups in Contemporary Physics
EditorsChengming Bai, Jean-Pierre Gazeau, Mo-Lin Ge
PublisherWorld Scientific Publishing
ISBN (Print)978-981-4518-57-4
Publication statusPublished - 2013

Publication series

NameNankai Series in Pure, Applied Mathematics and Theoretical Physics

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