Impurity Green's function of a one-dimensional Fermi-gas
  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. 
O. Gamayun, A. G. Pronko and M. B. Zvonarev
math-ph cond-mat.quant-gas math.MP nlin.SI