Correlations in one-dimensional quantum impurity problems with an external field Original Research Article

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 St(ω) for tunnelling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in χ″ (ω) and St (ω). Our results differ significantly from previous perturbative approaches.