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

Abstract

We establish the relation of the second virial coefficient of a recently proposed (μ[over ̃],q)-deformed Bose gas model [A. M. Gavrilik and Yu. A. Mishchenko, Ukr. J. Phys. 58, 1171 (2013)] to the interaction and compositeness parameters when either of these factors is taken into account separately. When the interaction is dealt with, the deformation parameter becomes linked directly to the scattering length and the effective radius of interaction (in general, to scattering phases). The additionally arising temperature dependence is a feature absent in the deformed Bose gas model within the adopted interpretation of the deformation parameters μ[over ̃] and q. Here the problem of the temperature dependence is analyzed in detail and its possible solution is proposed.

Correlation function intercepts forμ˜,q-deformed Bose gas model implying effective accounting for interaction and compositeness of particles

“…In this section we give an overview of the results from [3] where basing on [10,11] and on [13] the specially designed two-parameterμ, q-deformed Bose gas model capable to effectively describe the interacting gas of composite bosons was constructed. As we are interested in the effective description of interaction and compositeness effects existing in realistic gases, the model from [3,4] can serve as the "link" to the study of more microscopical aspects (including the involved parameters), especially in view of [4]. As mentioned, the corresponding DSF ϕμ ,q in (1) which determines the deformed Bose gas model to be considered in this section is the combination of previously studied ones, see [13] and the works [10,11].…”

“…The explicit virial coefficients with their dependence on the deformation parameters q andμ can in principle be related to the characteristic parameters linked directly/explicitly with the interaction between composite bosons as well as inside them (between their constituents), see [4].…”

“…Deformed Bose gas models based on a set of identical deformed (nonlinear) oscillators, or on deformed thermodynamic relations provide nonlinear extension of standard Bose gas model which finds applications to physical systems with one or more factors of non-ideality [1][2][3][4][5]. In general, the effective description or modeling of essentially nonideal (nonlinear) systems usually is performed by means of reexpressing of the physical quantities of the initial complicated system in terms of the analogous quantities of deformed model.…”

“…First steps to the (microscopics of) effective taking of interaction and compositeness jointly into account are made by introducing theμ, q-deformed Bose gas model [3,4] based on deforming the thermodynamics. Namely, in [3] theμ, q-deformed Bose gas model was realized through deforming the total mean number of particles or the partition function by means of the deformed analog of the derivative z d dz (z is fugacity) and use of the "hybrid" (combined) DSF…”

“…For that model, the deformed virial expansion was studied. In the sequel to [3], the relation of the obtained virial coefficients of the (μ, q)-deformed model (dependent explicitly on the deformation parametersμ and q) with scattering data of some interaction was explored [4], and the arising unusual temperature dependence ofμ and q discussed and justified. The version ofμ, q-deformed Bose gas model consid-ered herein uses for its definition the same DSF ϕμ ,q as in [3] (composed of quadratically nonlinear SF and the qdeformed one).…”