Within the framework of the theory of q-deformed bosons, we investigate the problem of fluctuations of a q-deformed boson system, and obtain the general result for thermodynamic fluctuations of such a system. Especially, for the system of a q-deformed boson gas, we get the expressions for the fluctuations of internal energy U and particle number N, and the correlation of the fluctuations of the two physical quantities above. Further numerical calculation shows that the fluctuations of such a q-deformed boson gas have some interesting features. We consider that this work may provide much insight into the theory of q bosons, and may also be useful for the further study of a concrete q-deformed boson gas.
An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.
In the framework of the q -deformed oscillator algebra we investigate the nature of the interaction among the particles of a free q -boson gas with a view to interpreting the interaction in terms of the general properties of the q -deformation. It is shown that many thermodynamic quantities characterizing the q -boson system can be expressed as power series in the number of particles operator or as a series in the deformation parameter q , implying that the q -deformation can originate from the interaction among the particles of the ensemble. As an example, we derive the virial expansion of the q -boson gas, showing that the lowest order coefficient reduces to the standard virial coefficient of an undeformed boson gas, while the higher order coefficients contain effects arising from interaction.
We present a comprehensive quantum many-body theory for
q-deformed fermions and bosons, offering a novel framework that relates particle statistics directly to effective interaction strength. Deformed by the parameters
k and
q, these particles exhibit statistical behaviors that interpolate between conventional bosonic and fermionic systems, enabling us to model complex interactions via statistical modifications. We develop a generalized Wick theorem and extended Feynman diagrammatics tailored to
kq particles, allowing us to calculate two types of Green's functions. Explicit expressions for these Green's functions are derived in both direct and momentum spaces, providing key insights into the collective properties of
q-fermionic and bosonic systems. Using a random-phase approximation, we estimate the dielectric function for
q-fermion gas ($k=\ensuremath{-}1$) and analyze the Friedel oscillations, the plasmon excitations, and the energy-loss function. Our results demonstrate that the effective interaction is tuned by the value of
q so that a noninteracting limit is obtained as $q\ensuremath{\rightarrow}0$, where the Friedel and the plasma oscillations disappear. An optimal value of
q, namely,
q∗, the plasma frequency, and the energy-loss function show an absolute maximum and the effective interaction changes behavior.
In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p,q-deformed bosons, in the corresponding p,q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p,q in the form symmetric under p<->q, and at p->1, q->1 turn into those known for usual bosons. Besides real parameters, we analyze the case of complex mutually conjugate p and q and find interesting implications. Also, the critical temperature is derived (for the p,q-Bose gas) and compared with the T_c of standard case of Bose condensation. Similar results are presented for the deformed Bose gas model of the Tamm-Dancoff type.