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Probability of phase separation for the Bose gas with delta interactions

V. Korepin·A. Its·A. Waldron
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Abstract

We consider the quantum Non-linear Schrödinger equation $i\partial_tΨ=-\partial_x^2Ψ+2cΨ^\daggerΨ^2$ 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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V. Korepin, A. Its, A. Waldron. 1995-10-12. Probability of phase separation for the Bose gas with delta interactions. https://arxiv.org/abs/cond-mat/9510068

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