The quantum non-linear Schrodinger model with point-like defect

Abstract

We establish a family of point-like impurities which preserve the quantum integrability of the non-linear Schrodinger model in 1+1 space-time dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the space-time symmetry of the bulk scattering matrix, are also discussed.

Comments on the integrability and the impurity free limit added

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• Sigma models in the presence of dynamical point-like defects
• Reflection-Transmission Quantum Yang-Baxter Equations
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• Type-I integrable quantum impurities in the Heisenberg model
• Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• A note on gl_N type-I integrable defects
• Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
• Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect
• Lax pair formulation in the simultaneous presence of boundaries and defects
• The sine-Gordon model in the presence of defects
• Factorization in integrable systems with impurity
• Non-Kirchhoff Vertices and NLS Ground States on graphs