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Solving the quantum non-linear Schrodinger equation with delta-type impurity

V. Caudrelier·M. Mintchev·E. Ragoucy
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Abstract

We establish the exact solution of the nonlinear Schrodinger equation with a delta-function impurity, representing a point-like 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.

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V. Caudrelier, M. Mintchev, E. Ragoucy. 2005-01-12. Solving the quantum non-linear Schrodinger equation with delta-type impurity. https://doi.org/10.1063/1.1842353

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