Impurity Green’s function of a one-dimensional Fermi-gas

O. Gamayun 1, 2 A. G. Pronko 3 M. B. Zvonarev 4

Nuclear Physics B, Elsevier, 2015, pp.83

We consider a one-dimensional gas of spin-1/2 fermions interacting through $\delta$-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function of the spin-down fermion. This impurity Green's function is represented in the thermodynamic limit as an integral of Fredholm determinants of integrable linear integral operators.

• 1. Bogolyubov Institute for Theoretical Physics, 14-b Metrolohichna street, Kiev 03680, Ukraine
• 2. Department of Physics, Lancaster University
• 3. Steklov Mathematical Institute
• 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques