From the Bose-Einstein to Fermion Condensation

A simple model of Bose-Einstein condensation of interacting particles is proposed. It is shown that in the condensate state the dependence of thermodynamic quantities on the interaction constant does not allow an expansion in powers of the coupling constant. Therefore it is impossible to pass to the Einstein model of condensation in an ideal Bose gas by means of a limiting passage, setting the interaction constant to zero. The account for the interaction between particles eli...

This short essay discusses the application of Bogoliubov's theory of superfluidity in the context of quantum phase transitions.

Arbitrarily large ground state population is a general property of any ideal bose gas when conditions of degeneracy are satisfied; it occurs at any dimension D. For $D = 1$, the condensation is diffuse, at $D = 2$ it is a sort of quasi-condensate. The discussion is made by following a microscopic approach and for finite systems. Some astrophysical consequences are discussed, as well as the temperature-dependent mass case.

A review on superfluidity and the BEC-BCS crossover in ultracold Fermi gases.

The elementary excitations in antiferromagnets are magnons, quasiparticles with integer spin and Bose statistics. In an experiment their density is controlled efficiently by an applied magnetic field and can be made finite to cause the formation of a Bose-Einstein condensate (BEC). Studies of magnon condensation in a growing number of magnetic materials provide a unique window into an exciting world of quantum phase transitions (QPT) and exotic quantum states.

Since the first experimental realization of Bose-Einstein condensation in cold atomic gases in 1995 there has been a surge of activity in this field. Ingenious experiments have allowed us to probe matter close to zero temperature and reveal some of the fascinating effects quantum mechanics has bestowed on nature. It is a challenge for mathematical physicists to understand these various phenomena from first principles, that is, starting from the underlying many-body Schr\"odin...

The possibility of the phenomenon of Bose condensation having a part to play in the discussion of neutron stars has been around for some time. Here the sorts of temperatures and densities that might be involved are discussed. Also, an alternative way of viewing the Bose condensation phenomenon is examined once more and, although found to lead to more accurate results in traditional examples, is found to have little numerical effect in astrophysical examples.

Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half- century old open problem in condensed matter physics, and raised new interrogations of their own.

The distinction between a classical liquid and a classical ordered solid is easy and depends on their different symmetries. The distinction between a classical glass and a classical liquid is more difficult, since the glass is also disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this article an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a...

We discuss the transition of fermion systems to a condensate of Bose dimers, when the interaction is varied by use of a Feshbach resonance. We argue that there is an intermediate phase between the superfluid Fermi gas and the Bose condensate of molecules, consisting of extended dimers.