Ansatz of Hans Bethe for a two-dimensional Bose gas

Details Ansatz of Hans Bethe for a two-dimensional Bose gas Ansatz of Hans Bethe for a two-dimensional Bose gas

2005-11-22

arxiv.org/abs/nlin/0511043v1

J. Phys. A: Math. Gen. 39 (2006) 3035-3045

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex2e, 12 pages

Scientific paper

10.1088/0305-4470/39/12/012

The method of q-oscillator lattices, proposed recently in [hep-th/0509181], provides the tool for a construction of various integrable models of quantum mechanics in 2+1 dimensional space-time. In contrast to any one dimensional quantum chain, its two dimensional generalizations -- quantum lattices -- admit different geometrical structures. In this paper we consider the q-oscillator model on a special lattice. The model may be interpreted as a two-dimensional Bose gas. The most remarkable feature of the model is that it allows the coordinate Bethe Ansatz: the p-particles' wave function is the sum of plane waves. Consistency conditions is the set of 2p equations for p one-particle wave vectors. These "Bethe Ansatz" equations are the main result of this paper.

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