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Solving the quantum nonlinear Schrodinger equation with delta-type impurity

Caudrelier, V., Mintchev, M. and Ragoucy, E. (2005). Solving the quantum nonlinear Schrodinger equation with delta-type impurity. Journal of Mathematical Physics, 46(4), doi: 10.1063/1.1842353

Abstract

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.

Publication Type: Article
Publisher Keywords: REFLECTION-TRANSMISSION ALGEBRAS, HALF-LINE, FIELD-THEORY, EXCHANGE ALGEBRAS, SCATTERING, DEFECT, QUANTIZATION, PARTICLES, SYSTEMS, MODELS
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/166
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Official URL: http://jmp.aip.org/

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