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

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

2004-04-20

arxiv.org/abs/math-ph/0404047v2

J.Math.Phys. 46 (2005) 042703

Physics

Mathematical Physics

31 pages; v2: proof in section 2.2 amended

Scientific paper

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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