  The phenomenon of Bose-like condensation, the continuous change of the
dimensionality of the particle distribution as a consequence of freezing out of
one or more degrees of freedom in the low particle density limit, is
investigated theoretically in the case of closed systems of massive bosons and
fermions, described by general single-particle hamiltonians. This phenomenon is
similar for both types of particles and, for some energy spectra, exhibits
features specific to multiple-step Bose-Einstein condensation, for instance the
appearance of maxima in the specific heat.
  In the case of fermions, as the particle density increases, another
phenomenon is also observed. For certain types of single particle hamiltonians,
the specific heat is approaching asymptotically a divergent behavior at zero
temperature, as the Fermi energy $\epsilon_{\rm F}$ is converging towards any
value from an infinite discrete set of energies: ${\epsilon_i}_{i\ge 1}$. If
$\epsilon_{\rm F}=\epsilon_i$, 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.
  PACS numbers: 05.30.Ch, 64.90.+b, 05.30.Fk, 05.30.Jp
