Nonlinear σ-models with noncompact symmetry group in the theory of a nearly ideal bose gas

O.K. Pashaev and S.A. Sergeenkov

Physica A: Statistical Mechanics and its Applications, 1986, vol. 137, issue 1, 282-294

Abstract: A classical version of the Heisenberg spin model on the noncompact SU(1,1)/U(1) manifold is constructed which is gauge equivalent to the NLSE. It is found that the gauge transformations generated by the Jost solutions to the NLSE linear problem allows one to obtain solutions of the appropriate σ-model. Spin-wave and soliton solutions and related energy, momentum and magnetization integrals are found. The spin-waves describe a precession motion on the pseudo-sphere S1,1 with the Bogolubov frequency, and the soliton solution describes a deviation from the precession motion plane. The soliton excitation spectrum when condensate density vanishes is reduced to that of the O(3) Heisenberg ferromagnet. In the case of unlimited length of the magnetization vector the first one gives rise to the hole excitation spectrum of an antiferromagnet, and magnetizations related to the upper and lower sheets of the hyperboloid compensate each other.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:137:y:1986:i:1:p:282-294

DOI: 10.1016/0378-4371(86)90076-2

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