Probability of phase separation for the Bose gas with delta interactions

Details Probability of phase separation for the Bose gas with delta interactions Probability of phase separation for the Bose gas with delta interactions

1995-10-12

arxiv.org/abs/cond-mat/9510068v1

Physics

Condensed Matter

12 pages, latex twice, to appear in the proceedings of the 19th IUPAP conference

Scientific paper

We consider the quantum Non-linear Schr\"{o}dinger equation $i\partial_t\Psi=-\partial_x^2\Psi +2c\Psi^\dagger\Psi^2$ with positive coupling constant $c$ varying from zero to infinity. We study quantum correlation functions of this model using the determinant representation of these correlation functions. We consider the case of a finite density ground state and evaluate, using the Riemann Hilbert problem, the asymptotics of the probability that no particles are present in the space interval $[0,x]$ in the large $x$ limit. We call this the probability of phase separation or alternately the emptiness formation probability.

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