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Impurity Green's function of a one-dimensional Fermi-gas (1410.1502v2)
Published 6 Oct 2014 in math-ph, cond-mat.quant-gas, math.MP, and nlin.SI
Abstract: 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.