Advances in Theoretical and Mathematical Physics

Volume 15 (2011)

Number 6

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

Pages: 1655 – 1743

DOI: http://dx.doi.org/10.4310/ATMP.2011.v15.n6.a3

Author

Karol Kajetan Kozlowski (Institut de mathématiques de Bourgogne, Université de Bourgogne)

Abstract

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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