Bosonic-fermionic degeneration

For the degenerate ground state, the wave function (10) is relevant only for bosons (deuterons), for the two particles in the same states are indistinguishable. For fermions (protons), spins are correlated in such a way that the total wave function is antisymmetrical with respect to particle permutations, according to the Pauli principle. The spatial wave function can be rewritten as... 

The origin of the nonvauishing Joule-Thomson effect is the effective repulsive (Fermions) and attractive (Bosons) potential exerted on the gas molecules, which arises from the different ways in which quantum states can be occupied in sy.stems obeying Fermi-Dirac and Boso-Einstein statistics, respectively [17]. In other words, the effective fields are a consequence of whether Pauli s antisymmetry principle, which is relativistic in nature [207], is applicable. Thus, a weakly degenerate Fermi gas will always heat up ((5 < 0), whereas a weakly degenerate Bose gas will cool down (5 > 0) during a Joule-Thomson expansion. These conclusions remain valid even if the ideal quantum gas is treated relativistically, which is required to understand... 

The same considerations also apply to the case of two open shells where the product of the fermion irreps for the open shells belongs to a doubly degenerate boson irrep. In this case the reference is a single determinant, related to its partner by the time-reversal operator. Because there is no symmetry between the open shells, we cannot derive relations between the amplitudes for Kramers partners. 

Fig. 8.2 A quantum degenerate gas of ultracold atoms reaches degeneracy when the matter waves of neighboring atoms overlap (a) at absolute zero, gaseous bosonic atoms all end up in the lowest energy state (b) fermions, in contrast, fill the states with one atom per state, and the energy of the highest filled state at T = 0 is the Fermi energy Ep ...

A Fermi-degenerate gas can coexist with a Bose-Einstein condensate. This was observed, for example, in experiments with an ultracold atomic mixture of Li atoms (bosons) and Li atoms (fermions) at a temperature of T = 0.28/l(K and Tf=0.2Tc, where Tp and Tc are the Fermi and the Bose-Einstein condensation critical temperature, respectively (Schreck et al. 2001). 

The possibility of pairing fermionic atoms (Cooper pairing) to form bosonic atoms has far-reaching consequences, as far as studies into such phenomena as superfluidity and superconductivity under the controlled conditions of quantum degenerate gases are concerned (see Section 8.5). 

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