Abstract
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 line shapes of the density of states are well described by a Lorentz type in both the resonances. These results are verified by another approach using a specific form of the scattering matrix to describe the scattering resonances.
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