Deformed Bose Gas Models Aimed at Taking into Account Both Compositeness of Particles and Their Interaction

Abstract

We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us to describe the interacting gas of composite (two-fermionic or two-bosonic) bosons. Using the relevant generalization of the Jackson derivative, we derive a two-parametric expression for the total number of particles, from which the deformed virial expansion of the equation of state is obtained. The latter is interpreted as the virial expansion for the effective description of a gas of interacting composite bosons with some interaction potential. K e y w o r d s: deformed oscillators, deformed Bose gas model, non-ideal Bose gas, virial expansion, modified Jackson derivative, virial coefficients, composite bosons.

Virial coefficients in the(μ̃,q)-deformed Bose gas model related to compositeness of particles and their interaction: Temperature-dependence problem

“…According to [4,13,[15][16][17][18]25,26], the virial coefficients within the DBGMs studied therein depend only on the deformation parameter(s), which in our interpretation are interrelated with nonideality factors and thus should not depend on the temperature. On the other hand, the virial coefficients for a gas with interaction manifest a temperature dependence [27].…”

“…We start with the recently obtained [15] deformed virial expansion for the (μ,q)-deformed Bose gas whose thermodynamics or statistical physics is given through the structure…”

“…Namely, in [15] the (μ,q)-DBGM is constructed so that ϕμ ,q (z d dz ) replaces the derivative z d dz in the known relation for the total number of particles given through the partition function, i.e., N = z d dz ln Z, yielding the definition for the deformed total number of particles in terms of the nondeformed partition functioñ…”

“…* omgavr@bitp.kiev.ua More recently it became clear that the possibility of realization (of operator algebra) of composite bosons by deformed bosons proven in [14] is naturally promoted to the elaboration of the DBGM able to effectively account for the compositeness of Bose particles (the compositeness makes them quasibosons, differing from strict bosons). Finally, let us mention recent work [15] that shows how to incorporate simultaneously two different factors of nonideality: the compositeness of particles and their interaction. That work motivated our present study.…”

“…In the present case the proximity of the virial expansion of the equation of state for the nonideal quantum gas to that of the DBGM is chosen as such a criterion. The structure function characterizing the DBGM of the effective description for the concreteness is taken to be of the same special form as in [15], however, the analogous consideration given below may concern a more general situation. This structure function is the functional composition of those corresponding to effectively taking the compositeness and interaction into account separately.…”