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n this article we study the Friedel phase of the electron transport in twodifferent systems of quantum dots which exhibit bound states in the continuum(BIC). The Friedel phase jumps abruptly in the energies of the BICs, which isassociated to the vanishing width of these states, as shown by Friedrich andWintgen in Phys. Rev. A \textbf{31}, 3964 (1985). This odd behavior of theFriedel phase has consequences in the charge through the Friedel sum rule.Namely, if the energy of the BIC drops under the Fermi energy the chargechanges abruptly in a unity. We show that this behavior closely relates withdiscontinuities in the conductance predicted for interacting quantum dotsystems.

Friedel phase discontinuity and bound states in the continuum in quantum dot systems