to the contribution of the wide fermionic density and of their self-interaction. From this figure it is clear that two fermionic states have lowered their energies by adjusting themselves into the potential well created by the BEC giving rise in this way to a [*matter wave quantum dot*]{} i.e. a localized BEC with one or more fermionic levels trapped inside.

![Time evolution of bosonic and fermionic densities in Fig. \[fig1\]a (left panel) and Fig. \[fig1\]c (right panel) obtained from the quasi-classical Eqs. (\[bose-fermi-eqns\]) on a line of length $L=40 \pi$. Space and time are in normalized units. []{data-label="fig2"}](fig2a.eps "fig:"){width="4.2cm" height="4.2cm"} ![Time evolution of bosonic and fermionic densities in Fig. \[fig1\]a (left panel) and Fig. \[fig1\]c (right panel) obtained from the quasi-classical Eqs. (\[bose-fermi-eqns\]) on a line of length $L=40 \pi$. Space and time are in normalized units. []{data-label="fig2"}](fig2b.eps "fig:"){width="4.2cm" height="4.2cm"}

Notice that the two level system exists at the bottom of the Fermi sea and are separated by a gap from other fermionic levels which rapidly became equally spaced, as one would expect for a parabolic trap. Also notice that the ground state energy of the bosonic part of the mixture is lowered inside the potential well corresponding to the 