Séminaire de Physique ThéoriqueIntegrable aspects of the mobile impurity
Oleksandr Gamayun (Université d'Amsterdam)
Thursday 06 December 2018 14:00 - Tours - Salle 1180 (Bât E2)
I will consider static and dynamic properties of the impurity immersed in the gas of one-dimensional spinless fermions (so-called McGuire model). This model is the simplest and yet non-trivial for capturing a peculiar physics and mathematics of the non-equilibrium processes. I will get an exact solution for the impurity's momentum distribution function and show that in a certain limit it the same as in the gas of hard-core anyons. It turns out that solution can be expressed in terms of the Fredholm determinants of integrable integral operators. I will explain a simple way to find asymptotic of the obtained expressions. Briefly, I will show how the same technique can be applied to describe dynamical phenomena such as incomplete impurity's relaxation and logarithmic diffusion.