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arXiv:hep-th/0404144 · Journal of Physics A Mathematical and General

The quantum nonlinear Schrödinger model with point-like defect

Vincent Caudrelier, Mihail Mintchev, E. Ragoucy

Published Jul 15, 2004• 35 citations
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Abstract

We establish a family of point-like impurities which preserve the quantum integrability of the nonlinear Schrödinger model in 1+1 spacetime 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 spacetime symmetry of the bulk scattering matrix, are also discussed.

DOI
10.1088/0305-4470/37/30/l02

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We establish the exact solution of the nonlinear Schrödinger equation with a delta-function impurity, representing a pointlike defect which reflects and transmits. We solve the problem both at the classical and the second quantized levels. In the quantum case the Zamolodchikov–Faddeev algebra, familiar from the case without impurities, is substituted by the recently discovered reflection-transmission (RT) algebra, which captures both particle–particle and particle–impurity interactions. The off-shell quantum solution is expressed in terms of the generators of the RT algebra and the exact scattering matrix of the theory is derived.
Nonperturbative exact solutions are allowed for quantum integrable models in one space-dimension. Going beyond this class we propose an alternative Lax matrix approach, exploiting the hidden multi-space–time concept in integrable systems and construct a novel nonlinear Schrödinger quantum field model in quasi-two dimensions. An intriguing field commutator is discovered, confirming the integrability of the model and yielding its exact Bethe ansatz solution with rich scattering and bound-state properties. The universality of the scheme is expected to cover diverse models, opening up a new direction in the field.
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