Correlations in one dimensional quantum impurity problems with an external field

Abstract

We study response functions of integrable quantum impurity problems with an external field at $T=0$ using non perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field dependent ground state, leading to renormalized (or ``dressed'') form-factors. We obtain exactly the low frequency behaviour of the dynamical susceptibility $χ''(ω)$ in the double well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem),and the low frequency behaviour of the AC noise $S_t(ω)$ for tunneling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in $χ''(ω)$ and $S_t(ω)$. Our results differ significantly from previous perturbative approaches.