Boosting the BEC critical temperature of an ideal Bose gas within a crystal with vacancies

We show that an ideal Bose gas in one or two-dimensional imperfect crystal presents Bose-Einstein condensation at a finite critical temperature, which does not happen when the crystal is perfect. For the three-dimensional imperfect crystal case, the BEC critical temperature is higher than that of the gas in the perfect crystal. We have obtained the energy spectrum of the particles using the transfer and dispersion matrix methods as well as the use of the Green function, transfer matrix and dispersion, which we use to calculate, in addition to the critical temperature, the specific heat for the Bose gas within imperfect two-dimensional structures such as multilines or grids, and for three-dimensional cases such as multiplanes, multitubes and multicubes.