Riemann--Hilbert approach to the time-dependent generalized sine kernel

Details Riemann--Hilbert approach to the time-dependent generalized sine kernel Riemann--Hilbert approach to the time-dependent generalized sine kernel

2010-11-25

arxiv.org/abs/1011.5897v2

Physics

Mathematical Physics

60 pages, 15 figures, V2: minor modifications in the introduction

Scientific paper

We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann--Hilbert based analysis.

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