  We discuss in more details the theory of low energy excitations in quantum
impurity problems with an external field at vanishing temperature, giving
further support to results of the previous paper. We then extend these results
to the next order at low frequency, obtaining in particular the exact
expression, as a function of the bias, of the first two derivatives of the
response function $\chi''(\omega)$ at $\omega=0$ in the double well problem of
dissipative quantum mechanics. We also extend our approach to the case of non
vanishing temperature and no external field. Fendley et al. had obtained in
that case an expression for the Hall conductance with a single impurity using a
Landauer-B\"uttiker type approach. We recover their result in the framework of
linear response theory using renormalized form-factors. We also obtain, as a
function of the temperature, the first derivative of the response function
$\chi''(\omega)$ at $\omega=0$ in the double well problem of dissipative
quantum mechanics.

Condensed Matter;High Energy Physics - Theory