Time Correlations in 1D Quantum Impurity Problems

We develop an analytical approach using form factors to compute time dependent correlations in integrable quantum impurity problems. As an example, we obtain for the first time the frequency dependent conductivity G(ω) for the tunneling between edges in the ν=1/3 fractional quantum Hall effect and the spectrum S(ω) of the spin-spin correlation in the anisotropic Kondo model and equivalently in the double well system of dissipative quantum mechanics, both at vanishing temperature.