The transition from bulk to nano as a phase transition

It is demonstrated that the chemical potential of bosons trapped in a harmonic potential shows a discontinuity as a function of the number of particles in the system. In the model used, it is shown that if the number of particles is of the order of 10⁶ or greater, bulk-like behaviour is exhibited by the system. This translates to a ratio of V/V_c>10⁶ for bulk behaviour, where V is the crystallite volume of the experimental sample and V_c is the volume of the unit cell. Several experimental results covering a wide range of physical phenomena that corroborate the fact that such a number-induced phase transition indeed exists are presented.