Student Workshop on Integrability

Long-time and large-distance asymptotics of Fredholm determinant representations of correlation functions at finite temperature

Not scheduled

2h

Eötvös Room, Northern Building

Poster Poster

Speaker

Mikhail Minin (Bergische Universität Wuppertal)

Description

The study of correlation functions of integrable models at their free fermion points often leads to expressions involving Fredholm determinants of integrable integral operators. This occurs, for example, in dynamical two-point correlation functions of the impenetrable Bose gas, the XY and XX spin chains at finite temperature. In this talk, we address the problem of obtaining the long-time and large-distance asymptotics of Fredholm determinants of this type, using Riemann–Hilbert techniques. We present the asymptotic analysis in detail in a generalized setting and apply the resulting asymptotic expansion explicitly to the field–field correlation function of the impenetrable Bose gas.
This talk is based on joint work with Frank Göhmann and Karol Kozlowski.