Tuning the transmission phase by the dot size

The phase shift of the electron's wave function after a tunneling event (i.e. the transmission phase) was at first measured for its fundamental or applicative relevance for quantum circuitry, but later the phase study self-motivated due to a number of unexpected results. One such result was the reduced increment of the phase on some resonances - with only fractions of π - in the few-electrons “mesoscopic” regime. In this paper we address such a regime for a rectangular quantum dot and compute the total phase increase on the first four resonances by means of accurate configuration-interaction method and a generalized Friedel sum rule as proposed by Rontani (2006) [17]. Our findings confirm that the electronic correlations reduce the on-resonance phase growth which is also found to decrease quasi-linearly with the dot size, the decrease being more pronounced as the number of electrons on the dot is raised. Sudden jumps (of small amplitude) of the phase are found to accompany ground states spin transitions.