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arXiv:math-ph/9811009 · Theoretical and Mathematical Physics

On the Riemann-Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear schrödinger equation: Interacting fermion case

Alexander Rudol'fovich Its, N. A. Slavnov

Published May 1, 1999• 19 citations
arXivHTMLPDF
DOI
10.1007/bf02557351

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We consider the quantum Non-linear Schrödinger equation i∂tΨ=−∂x2Ψ+2cΨ†Ψ2i\partial_tΨ=-\partial_x^2Ψ+2cΨ^\daggerΨ^2i∂t​Ψ=−∂x2​Ψ+2cΨ†Ψ2 with positive coupling constant ccc 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][0,x][0,x] in the large xxx limit. We call this the probability of phase separation or alternately the emptiness formation probability.