Conductance and density of states as the Kramers-Kronig dispersion relation

By applying the Kramers-Kronig dispersion relation to the transmission amplitude a direct connection of the conductance with the density of states is given in quantum scattering systems connected to two one-channel leads. Using this method we show that in the Fano resonance the peak position of the density of states is generally different from the position of the corresponding conductance peak, whereas in the Breit-Wigner resonance those peak positions coincide. The lineshapes of the density of states are well described by a Lorentz type in the both resonances. These results are verified by another approach using a specific form of the scattering matrix to describe scattering resonances.