Solving the quantum nonlinear Schrodinger equation with delta-type impurity

Article, Preprint English OPEN
Caudrelier, V. ; Mintchev, M. ; Ragoucy, E. (2005)
  • Publisher: American Institute of Physics
  • Related identifiers: doi: 10.1063/1.1842353
  • Subject: QC | Mathematical Physics | High Energy Physics - Theory | Mathematics - Quantum Algebra | 82B23, 81R50

We establish the exact solution of the nonlinear Schrodinger 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. (C) 2005 American Institute of Physics.
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