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arXiv:cond-mat/9402086

Bethe Ansatz and Quantum Davey-Stewartson 1 System with Multicomponent in Two Dimensions

Yi Cheng, Mu-Lin Yan, Bao‐Heng Zhao

Published Feb 21, 1994• 0 citations
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Abstract

The quantum 2-component DS1 system was reduced to two 1D many-body problems with $δ-$function interactions, which were solved by Bethe ansatz. Using the ansatz in ref.[1] and introducing symmetric and antisymmetric Young operators of the permutation group, we obtain the exact solutions for the system.

DOI
10.48550/arxiv.cond-mat/9402086

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The quantum 2-component DS1 system was reduced to two 1D many-body problems with δ−δ-δ−function interactions, which were solved by Bethe ansatz. Using the ansatz in ref.[1] and introducing symmetric and antisymmetric Young operators of the permutation group, we obtain the exact solutions for the system.
The quantum 2-component DS1 system in two dimensions has been reduced to two 2-component many-body problems both in one dimension by an analogue of the method of separation of variables. The solutions to 2 dimensional problem under consideration can be constructed from the resulting problem in one dimensions. For latters with the delta\\deltadelta-function interactions and being solved by the Bethe ansatz, we introduce symmetrical and antisymmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system.
The Davey-Stewartson 1 (DS1) system [Proc. R. Soc. London, Ser. A 338, 101 (1974)] is an integrable model in two dimensions. A quantum DS1 system with two color components in two dimensions has been reformulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with two color components. The solutions to the two-dimensional problem under consideration can be constructed from the resulting problem in one dimensions. For the latter problem with delta-function interactions and solution by the Bethe ansatz, we introduce symmetrical and antisymmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system.
A quantum N-body problem with 2-component in (2 + 1) dimensions deduced from an integrable model in (2 + 1) dimensions is investigated. The Davey–Stewartson 1 (DS1) system9 is an integrable model in two dimensions. A quantum DS1 system with 2 color components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 color components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in one dimension. For the latter with δ-function interactions and being solved by the Bethe–Yang ansatz, we introduce symmetrical and anti-symmetrical Young operators of the permutation group and obtain the exact solutions for the quantum DS1 system. The application of the solutions is discussed.
The repulsive $\ensuremath{\delta}$ interaction problem in one dimension for NNN particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations RRR of the permutation group SN{S}_{N}SN​. For some R′sR'\mathrm{s}R′s this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-\textonehalf{} fermions is reduced to a generalized Fredholm equation.