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

Vincent Caudrelier (1) , Eric Ragoucy (1)

1 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

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.

Mots clés: Systemes Intégrables avec défauts; Equation de Schrödinger non-linéaire; Brisure de Symétrie

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Autre [cond-mat.other]; Physique mathématique [math-ph]

Vincent Caudrelier, Eric Ragoucy. Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect. Journal of Physics A: Mathematical and Theoretical, 2005, 38, pp.2241. ⟨hal-00003223v2⟩