PreprintCC BY 4.0arXiv
Finite temperature Fredholm determinants for dynamical correlation functions
Abstract
We study the long-time, large-distance asymptotics of finite-temperature dynamical Fredholm determinants using effective form factors. The method expresses these asymptotics as a functional of an effective phase shift. We determine its two branches on either side of a quadratic stationary point and the transition profile joining them. The profile is expressed through parabolic-cylinder functions. Its connection to the high-temperature Gaussian β ensemble fixes the finite normalization, in agreement with an independent Riemann--Hilbert analysis. We also show that the leading exponential asymptotics suffice to recover the Euler-scale prediction of generalized hydrodynamics for the dynamical structure factor of hard rods.
Related
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BibTeX
@misc{gamayun2026finite,
title = {{Finite temperature Fredholm determinants for dynamical correlation functions}},
author = {Oleksandr Gamayun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18750},
eprint = {2610.18750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18750},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite temperature Fredholm determinants for dynamical correlation functions
AU - Oleksandr Gamayun
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.18750
UR - https://arxiv.org/abs/2610.18750
AB - We study the long-time, large-distance asymptotics of finite-temperature dynamical Fredholm determinants using effective form factors. The method expresses these asymptotics as a functional of an effective phase shift. We determine its two branches on either side of a quadratic stationary point and the transition profile joining them. The profile is expressed through parabolic-cylinder functions. Its connection to the high-temperature Gaussian β ensemble fixes the finite normalization, in agreement with an independent Riemann--Hilbert analysis. We also show that the leading exponential asymptotics suffice to recover the Euler-scale prediction of generalized hydrodynamics for the dynamical structure factor of hard rods.
ER -