## 5 Conclusions  
We have constructed a model of an excitonic dimer of QDs including both local and CT excitons that aimed at demonstrating the electronic coherence dynamics at the level of an ensemble that takes into account the inherent size dispersion of the individual QDs. Because of the inevitable size dispersion, each dimer is made of not exactly the same QDs, which leads to dispersion of the zero order exciton energies, Coulomb matrix elements, and transition dipoles. The size dispersion induces accidental resonances between the energy levels of the two QDs that can lead to a strong effective interdot coupling between local excitons; this is particularly the case when the excitonic bands are engineered to overlap by tuning the size of the QDs, with the largest effect being obtained in the case of a homodimer. We focused on dimers of small CdSe QDs, with diameters in the range of 2 to 4 nm. Provided that an accurate parametrization of the Hamiltonian is available, our approach is general and could be applied to other colloidal QDs.  
Excitation by short fs pulses allows building superpositions of eigen excitons, which leads to interdot coherent energy transfer and charge migration. We show that the spectroscopic signature of excitonic coherence beatings is strong at the level of the ensemble and could be measured. Transition absorption spectra averaged over the ensemble allow probing two different time scales for the coherent beatings. These could also be probed using 2D electronic spectroscopy, as has already been done for solutions of isolated QDs [25; 26; 28; 29; 30; 31; 32]. The short few fs periods correspond to GS-exciton coherences, while the longer ones in the 10-20 fs range correspond to coherences between local excitons, which lead to charge migration and coherent energy transfer. There are also inter exciton coherences with much longer periods, in the range of dozens of fs. These inter exciton coherences will couple to the low frequency phonon and acoustic modes [24; 82; 83; 88]. The large density of purely excitonic coherences occurring on a wide range of time scale can be controlled by selecting the mean size of the two QDs used to make the dimer. The ultrafast charge migration and interdot motion of the electronic density can be controlled by tuning the sequence of ultrashort fs laser pulses before the onset of dephasing owing to the coupling to the environment and to the phonon modes, opening the way to applications to light harvesting [12; 13; 89; 90] and information processing devices [59; 73; 91].  
The following are available online at [[http://www.mdpi.com/2076-3417/10/4/1328/s1](http://www.mdpi.com/2076-3417/10/4/1328/s1)]([http://www.mdpi.com/2076-3417/10/4/1328/s1](http://www.mdpi.com/2076-3417/10/4/1328/s1)), Figure S1-Figure S1, Table S1.  
Conceptualization, F.R., H.G., B.F., and R.D.L.; methodology, F.R., H.G., B.F., and R.D.L.; software, H.G.; formal analysis, F.R., H.G., B.F., and R.D.L.; writing--original draft preparation, F.R. and H.G., writing--review and editing, F.R., H.G., B.F., and R.D.L. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the FET open EC project COPAC #766563 and the Fonds National de la Recherche Scientifique (F.R.S-FNRS, Belgium), #T0.205.20. Computational resources have been provided by the Consortium des Equipements de Calcul Intensif (CECI), funded by the F.R.S-FNRS under Grant #2.5020.11. B.F. acknowledges the support of the Ministero dell'Istruzione, Universita e Ricerca through the grant [PERSON] (2013).  
The authors declare no conflict of interest.