Dimensionality effects in restricted bosonic and fermionic systems

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.JpComment: 7 pages, 3 figures (included

Identifying, Estimating and Testing Restricted Cointegrated Systems: An Overview

The notion of cointegration has lead to a renewed interest in the identification and estimation of structural relations among economic time series, a field to which Henri Theil has made many pioneering contributions. This paper reviews the different approaches that have been put forward in the literature for identifying cointegrating relationships and imposing (possibly over-identifying) restrictions on them. Next, various algorithms to obtain (approximate) maximum likelihood estimates and likelihood ratio statistics are reviewed, with an emphasis on so-called switching algorithms. The implementation of these algorithms is discussed and illustrated using an empirical example.