Quench Dynamics of the Gaudin-Yang Model

Abstract

We study the quench dynamics of one dimensional bosons or fermion quantum gases with either attractive or repulsive contact interactions. Such systems are well described by the Gaudin-Yang model which turns out to be quantum integrable. We use a contour integral approach, the Yudson approach, to expand initial states in terms of Bethe Ansatz eigenstates of the Hamiltonian. Making use of the contour, we obtain a complete set of eigenstates, including both free states and bound states. These states constitute a larger Hilbert space than described by the standard String hypothesis. We calculate the density and noise correlations of several quenched systems such as a static or kinetic impurity evolving in an array of particles.