AI 中文总结
本文对与Lieb-Liniger玻色气体关联函数相关的带广义正弦核的可积积分算子Fredholm行列式开展大x渐近分析，依托矩阵Riemann-Hilbert问题，适配有限温度及任意正耦合常数的关联函数研究。
AI 中文摘要
我们对具有广义正弦核的可积积分算子的Fredholm行列式进行了大x渐近分析，其中x控制着算子沿积分轮廓的振荡强度，在应用于可积量子系统关联函数时将作为距离变量。我们的广义正弦核包含多个函数参数，这使我们能够将其适配于有限温度下、所有正耦合常数取值的Lieb-Liniger模型动力学关联函数分析，也能处理由广义吉布斯系综支配的一类平衡关联函数。本研究基于与该可积积分算子正则关联的矩阵Riemann-Hilbert问题分析。
英文摘要
We perform a large-$x$ asymptotic analysis of the Fredholm determinant of an integrable integral operator with generalized sine kernel, where $x$ controls the strength of the oscillations along the integration contour of the operator and will play the role of the distance variable in applications to the correlation functions of integrable quantum systems. Our generalized sine kernel involves a number of functional parameters that will allow us to adapt it to the analysis of the dynamical correlation functions of the Lieb--Liniger model at finite temperature and for all positive values of the coupling constant. It will also allow us to consider a class of equilibrium correlation functions that are governed by generalized Gibbs ensembles. Our work is based on the analysis of a matrix Riemann--Hilbert problem that is canonically connected with our integrable integral operator.
Comments87 pages, typos corrected
