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

Source: [Riemann--Hilbert approach to the time-dependent generalized sine kernel](<https://www.sota2.com/research/paper/68fa2ec21e209131ce865e8f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T17:07:11.912Z

Authors: K. K. Kozlowski

Published: 2010-11-25T22:45:11.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1011.5897>)

[PDF](<https://arxiv.org/pdf/1011.5897.pdf>)