Analytic solutions of the 1D finite coupling delta function Bose gas

Details Analytic solutions of the 1D finite coupling delta function Bose gas Analytic solutions of the 1D finite coupling delta function Bose gas

2006-07-21

arxiv.org/abs/cond-mat/0607542v2

Physics

Condensed Matter

Statistical Mechanics

23 pages, 0 figures, uses rotate.sty. A few lines added. Accepted by Phys. Rev. A

Scientific paper

10.1103/PhysRevA.74.043614

An intensive study for both the weak coupling and strong coupling limits of the ground state properties of this classic system is presented. Detailed results for specific values of finite $N$ are given and from them results for general $N$ are determined. We focus on the density matrix and concomitantly its Fourier transform, the occupation numbers, along with the pair correlation function and concomitantly its Fourier transform, the structure factor. These are the signature quantities of the Bose gas. One specific result is that for weak coupling a rational polynomial structure holds despite the transcendental nature of the Bethe equations. All these new results are predicated on the Bethe ansatz and are built upon the seminal works of the past.

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