Orateur
Description
Dynamical two-point correlation functions encode the response to local perturbations, determine the transport coefficients, and connect the microscopic quantum mechanical description to experimentally observable quantities. Obtaining their long-time, large-distance asymptotics for systems in thermal or non-thermal equilibrium is an open problem even for integrable models. We present results for the Lieb--Liniger model at infinite repulsion (the impenetrable Bose gas), covering a large class of non-thermal equilibrium conditions and extending previous results for the thermal equilibrium case. Starting from exact representations of the correlation functions as Fredholm determinants of an integrable integral operator depending parametrically on distance $x$, time $t$, and on the filling fraction characterizing the equilibrium conditions, we perform a rigorous asymptotic analysis using Riemann–Hilbert techniques. We identify two classes of filling fractions, characterized by the number of poles on the real axis (a generalization of Fermi points) contributing together with the unique saddle point to the asymptotic expansion. For each class, we derive the asymptotic expansion in powers of $x^{-1/2}$ as $x, t \to \infty$ at fixed $x/t$, with closed-form expressions for the leading and sub-leading terms, logarithmic corrections, and overall constants.
Based on joint work with Frank Göhmann and Karol K. Kozlowski (arXiv:2608.16727), and on ongoing work with the same authors and Alexander Weiße.