On the Quantization of the Monoatomic Ideal Gas

We outline Fermi's early attitude towards old quantum physics. We sketch out the context from which his interest for quantum physics arose, and we deal with his work on quantum statistics. We also go through the first two courses on theoretical physics he held in Rome, and his 1928 book on atomic physics.

The aim of this Tutorial is to present the basic mathematical techniques required for an accurate description of cold trapped atoms, both Bose and Fermi. The term {\it cold} implies that considered temperatures are low, such that quantum theory is necessary, even if temperatures are finite. And the term {\it atoms} means that the considered particles are structureless, being defined by their masses and mutual interactions. Atoms are {\it trapped} in the sense that they form a...

We predict novel phenomena in the behavior of an ultra- cold, trapped gas of fermionic atoms. We find that quantum statistics radically changes the collisional properties, spatial profile, and off-resonant light scattering properties of the atomic fermion system, and we suggest how these effects can be observed.

We propose a method to study the degeneracy of a trapped atomic gas of fermions through the relaxation of the motion of a test particle. In the degenerate regime, and for an energy of the test particle well below the Fermi energy, we show that the Fermi-Dirac statistics is responsible for a strong decrease of the relaxation rate. This method can be used to directly measure the temperature of the fermionic gas.

We have analytically explored thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials of the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become plausible specially in the intermediate regime between the classical and quantum limits.

This manuscript studies harmonically trapped ideal Bose and Fermi gas systems and their thermodynamics in the framework of the Extended Uncertainty Principle (EUP). In particular, we reveal how the ground and thermal particle ratios, condensate temperature, internal energy, specific heat and equation of state functions change in the EUP formalism. Nevertheless, we conclude that, in contrast to the effects of the Gravitational (Generalized) Uncertainty Principle (GUP), the EUP...

We point out an important hidden inconsistency in Fermi's probability of the quantum states that engendered inconsistent/inaccurate equations-of-state extensively used in the literature to model nonideal plasma systems. The importance of this amendment goes beyond rectifying our comprehension and foundation of an important physical problem to influencing contemporary research results.

The ideal (i.e. noninteracting), homogeneous Fermi gas, with its characteristic sharp Fermi surface in the momentum distribution, is a fundamental concept relevant to the behavior of many systems. With trapped Fermi gases of ultracold atoms, one can realize and probe a nearly ideal Fermi gas, however these systems have a nonuniform density due to the confining potential. We show that the effect of the density variation, which typically washes out any semblance of a Fermi surf...

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924-1925. Although it failed to attract the attention of Einstein's contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein's quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its amb...

Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the fundamental ensembles of statistical physics avoiding any limiting procedures, quantum hypothesis and even statistical entropy maximization. This point of view leads also to some related classes of correlated particle statistics.