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We develop a method to approach quantum gases of quasiparticles with generalized statistics. This way is based on Fibonacci hierarchies and offers an alternative issue to the Haldane–Wu method. We give the statistical weights densities ρ_M of gases of quasiparticles with s = 1/M : mod(1), M ≥ 2, using the combinatorial aspects of M-generalized Fibonacci series. This is a remarkable feature which envelopes naturally the Fermi and Bose statistics.

DAMA/NaI and DAMA/LIBRA data have allowed the study of several rare processes. In this paper, the results obtained for internal pair production in ${}^{241}$Am $\alpha$ decay, charge not conserving electron capture in ${}^{127}$I and possible processes violating the Pauli Exclusion Principle are briefly discussed.

Motivated by the recent interest in underground experiments phenomenology (see Refs. 1–3), we review the main aspects of one specific noncommutative space–time model, based on the Groenewold–Moyal plane algebra, the $𝜃$-Poincaré space–time. In the $𝜃$-Poincaré scenario, the Lorentz co-algebra is deformed introducing a noncommutativity of space–time coordinates. In such a theory, a new quantum field theory in noncommutative space–time can be reformulated. Tackling on several conceptual misunderstanding and technical mistakes in the literature, we will focus on several issues such: (i) the construction of fields theories in $𝜃$-Poincaré; (ii) the unitarity of the S-matrix; (iii) the violation of locality, (iv) the violation of the spin-statistic theorem and the Pauli principle; (v) the observables for underground experiments.

A physical interpretation is given to a curious "hump" that develops in the chemical potential as a function of absolute temperature in an ideal Fermi gas for any spatial dimensionality d < 2, integer or not, in contrast with the more familiar monotonic decrease for all d ≥ 2. The hump height increases without limit as d decreases to zero. The divergence at d = 0 is shown to be a clear manifestation of the Pauli Exclusion Principle whereby two spinless fermions cannot sit on top of each other in configuration space. The hump itself is thus an obvious precursor of this manifestation, otherwise well understood in momentum space. It also constitutes an "ideal quantum dot" when d = 0.

In this paper the transport properties of normal-ferromagnetic-normal graphene structures are studied by the Landauer Büttiker approach. The properties of spin chiral ferromagnetic layer are investigated when exchange energy exceeds the Fermi energy. To this end, the conductance as well as the shot noise are calculated. The Pauli exclusion principle that acts only on the carriers with the same spin, reduces the shot noise from its Schottky value. The effects of shot noise on the carriers with opposite spins in a ferromagnetic graphene are considered and it is observed that in this case the shot noise is lower than that of non-graphene systems since the quasiparticles with opposite spins are correlated due to chirality. In this way we report a new source of fluctuations in spin chiral materials.

In terms of an exact equation for the thermodynamic potential due to interaction between two particles and based on Green's function method; we have derived the Landau expansion of the thermodynamic potentials in terms of the variation of the quasiparticle distribution function. We have also derived the expansion of the thermodynamic potential in terms of the variation of an exact single particle (not quasiparticles), this derivations lead to the relationship between the interaction function for two quasiparticles and the interaction energy between two particles as shown. Further, in terms of the four-point vertex part we are led to the Pauli exclusion principle.

The Pauli Exclusion Principle (PEP) represents one of the fundamental principles of the modern physics and our comprehension of the surrounding matter is based on it. Even if today there are no compelling reasons to doubt its validity, it still spurs a lively debate on its limits, as testified by the abundant contributions found in the literature and in topical conferences. We present a method of searching for possible small violations of PEP for electrons, through the search for "anomalous" X-ray transitions in copper atoms, produced by "fresh" electrons which can decay in a Pauli-forbidden transition to the 1s level, already occupied by two electrons. The VIP Experiment has the scientific goal to improve by four orders of magnitude the present limit on the probability of PEP violation for electrons, bringing it into the 10^-30–10^-31 region. Preliminary results, together with future plans, are presented.

A physical interpretation is given to a curious "hump" that develops in the chemical potential as a function of absolute temperature in an ideal Fermi gas for any spatial dimensionality d < 2, integer or not, in contrast with the more familiar monotonic decrease for all d ≥ 2. The hump height increases without limit as d decreases to zero. The divergence at d = 0 is shown to be a clear manifestation of the Pauli Exclusion Principle whereby two spinless fermions cannot sit on top of each other in configuration space. The hump itself is thus an obvious precursor of this manifestation, otherwise well understood in momentum space. It also constitutes an "ideal quantum dot" when d = 0.