Geometric Aspects and Some Uses of Deformed Models of Thermostatistics

Abstract

Abstract:We consider diverse deformed Bose gas models (DBGMs) focusing on distributions and correlations of any order, and also on deformed thermodynamics. For so-called µ-deformed Bose gas model (µ-DBGM), main thermodynamic aspects are treated: total number of particles, deformed partition function, etc. Using a geometric approach, we confirm the existence of critical behavior-Bose-like condensation; we find the critical temperature T (µ) c depending on µ so thatfor µ > 0. This fact and other advantages of µ-DBGM relative to the usual Bose gas, e.g., stronger effective inter-particle attraction (controlled by the parameter µ), allow us to consider the condensate in µ-DBGM as a candidate for modeling dark matter. As another, quite successful application we discuss the usage of the two-parameter (μ, q)-deformed BGM for effective description of the peculiar (non-Bose like) behavior of two-pion correlations observed in the STAR experiment at RHIC (Brookhaven). Herein, we point out the transparent role of the two deformation parametersμ and q as being responsible for compositeness and (effective account of) interactions of pions, respectively.

q-Deformed quantum mechanics related to the Tamm-Dancoff oscillator algebra and some physical applications

“…It is surely beyond doubt that the Jackson's q-calculus plays a key role in the construction of representations of quantum groups [3][4][5] as well as their associated algebras [6][7][8][9][10][11][12][13][14]. In recent years, deformed Bose and deformed Fermi gas models based on their respective deformed particle algebras (either bosonic or fermionic) have been applied to different aspects of physical phenomena such as in treating the unstable phonon spectrum of 4 He [15], probing higherorder effects in the many-body interactions in nuclei [16], effective modeling of dark matter [17][18][19], addressing the deformed quantum statistics of charged, extremal black holes [20,21], and effective description of the observed non-Bose type behavior of the intercept of the two-particle correlation function of identical pions produced in relativistic heavy-ion collisions [22][23][24][25]. One interesting question in the same research direction has been put forward by the works of [26,27] about whether the possibility of interpreting a q-deformed noninteracting system as incorporating the effects of interactions among its particles.…”