Temperature-fermion number correlations in finite paired systems

Abstract

We investigate finite systems of N paired fermions, common in atomic nuclei, for example. These systems exhibit quantum mechanical features akin to those of superconductors. We discover, however, some specific N dependent effects that can not be attained in the thermodynamics limit of ordinary superconductivity. In particular, an important fact is uncovered: there is a strong correlation between the temperature T and the number of fermions N. A certain temperature increase ∆T produces, in thermal quantifiers (such as the entropy), quite different effects if N = 4 or N = 25. In fact, whether a given temperature value should be regarded as high or low can not be ascertained independent of the N value.