Dimensionality effects in restricted bosonic and fermionic systems

The phenomenon of Bose-Like condensation, the continuous change of the dime nsionality of the particle distribution as a consequence of freezing out of one or more degrees of freedom in the limit of tow particle density, is in vestigated theoretically in the case of closed systems of massive bosons an d fermions, described by general single-particle Hamiltonians. This phenome non is similar for both types of particles and, for some energy spectra, ex hibits features specific to multiple-step Bose-Einstein condensation, for i nstance, the appearance of maxima in the specific heat. In the case of ferm ions, as the particle density increases, another phe phenomenon is also obs erved. For certain types of single particle Hamiltonians, the specific heat is approaching asymptotically a divergent behavior at zero temperature, as the Fermi energy epsilon (F) is converging towards any value from an infin ite discrete set of energies {epsilon (i)}(i less than or equal to1). If ep silon (F) = epsilon (i), for any i, the specific heat is divergent at T = 0 just in infinite systems, whereas for any finite system the specific heat approaches zero at low enough temperatures. The results are particularized for particles trapped inside parallelepipedic boxes and harmonic potentials .