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Quantum Integrable System with Multi-components in Two-Dimension

Mu-Lin Yan·Bao-Heng Zhao
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Abstract

A quantum N-body problem with 2-component in (2+1)-dimension deduced from integrable model in (2+1) dimension is investigated. The Davey-Stewartson 1(DS1) system[Proc. R. Soc. London, Ser. A {\bf 338}, 101 (1974)] is an integrable model in two dimensions. A quantum DS1 system with 2 colour-components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 colour-components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimensions. For latters with the $δ$-function interactions and being solved by the Bethe-Yang ansatz, we introduce symmetrical and antisymmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system. The application of the solusions is discussed.

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Mu-Lin Yan, Bao-Heng Zhao. 2002-09-02. Quantum Integrable System with Multi-components in Two-Dimension. https://doi.org/10.1142/s021798490200441x

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