Physics – Mathematical Physics
Scientific paper
2004-11-04
J.Phys. A38 (2005) 2241-2258
Physics
Mathematical Physics
discussion on symmetry breaking has been improved and examples added
Scientific paper
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.
Caudrelier Vincent
Ragoucy Eric
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