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Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect

Caudrelier, V. & Ragoucy, E. (2005). Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect. Journal of Physics A: Mathematical and General, 38(10), pp. 2241-2257. doi: 10.1088/0305-4470/38/10/013


We introduce and solve the one-dimensional quantum non-linear Schrodinger (NLS) equation for an N-component field defined on the real line with a defect sitting at the origin. The quantum solution is constructed using the quantum inverse scattering method based on the concept of reflection-transmission (RT) algebras recently introduced. The symmetry of the model is generated by the reflection and transmission defect generators defining a defect subalgebra. We classify all the corresponding reflection and transmission matrices. This provides the possible boundary conditions obeyed by the canonical field and we compute these boundary conditions explicitly. Finally, we exhibit a phenomenon of spontaneous symmetry breaking induced by the defect and identify the unbroken generators as well as the exact remaining symmetry.

Publication Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and General. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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