N ov 2 00 1 Ouantum integrable system with two color components in two dimensions ∗
نویسنده
چکیده
The Davey-Stewartson 1(DS1) system[9] 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 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.
منابع مشابه
N ov 2 00 6 A hierarchy of integrable PDEs in 2 + 1 dimensions associated with 2 - dimensional vector fields
We introduce a hierarchy of integrable partial differential equations in 2 + 1 dimensions arising from the commutation of 2 dimensional vector fields, and we construct the formal solution of the associated Cauchy problems using the Inverse Scattering Transform for one-parameter families of vector fields recently introduced in [1, 2]. Due to the ring property of the space of eigenfunctions, the ...
متن کاملX iv : h ep - t h / 04 11 26 1 v 1 2 9 N ov 2 00 4 Spin bits at two loops
We consider the Super Yang–Mills/spin system map to construct the SU(2) spin bit model at the level of two loops in Yang–Mills perturbation theory. The model describes a spin system with chaining interaction. In the large N limit the model is shown to be reduced to the two loop planar integrable spin chain.
متن کامل/ 99 06 15 7 v 2 2 6 D ec 1 99 9 A Quantum Integrable System with Two Colour - Components in Two Dimensions ∗
The Davey-Stewartson 1(DS1) system[9] 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 o...
متن کاملar X iv : 0 71 1 . 04 90 v 1 [ nl in . S I ] 4 N ov 2 00 7 Two new multi - component BKP hierarchies
We firstly propose two kinds of new multi-component BKP (mcBKP) hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources which Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k−constrained BKP hierarchy and to integrable (1+1)-dimensiona...
متن کاملar X iv : c on d - m at / 0 21 14 34 v 1 2 0 N ov 2 00 2 Solutions of the Gross - Pitaevskii equation in two dimensions
In two dimensions the Gross-Pitaevskii equation for a cold, dilute gas of bosons has an energy dependent coupling parameter describing particle interactions. We present numerical solutions of this equation for bosons in harmonic traps and show that the results can be quite sensitive to the precise form of the coupling parameter that is used. Solutions of the Gross-Pitaevskii equation in two dim...
متن کامل