An interacting ensemble of particles in the context of quantum algebra

Abstract

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 qdeformation. It is shown that many thermodynamic quantities characterizing the q-boson system can be expressed as power series in the number of particles operator N 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.

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].…”

“…Somewhat earlier, the Arik-Coon structure function [N ] q was used to effectively incorporate [13] the interaction between the particles of a gas of elementary bosons.…”

“…It was demonstrated [12] that the nonpointlike form of particles may serve as the first and most obvious such factor and it is possible to link the parameter q of deformation directly with the ratio of the excluded volume (the sum of nonzero proper volumes of the particles) to the whole volume. The next factor of nonideality is the interaction between the particles and as shown in [13] it can be naturally taken into account by a version of deformation. * 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).…”

Negentropy in Many-Body Quantum Systems

“…If the systems are non-ideal, the distribution functions change, due to the presence of particle correlations beyond the ideality. This requires the introduction of q-or κ-Fermi-Dirac and q-or κ-Bose-Einstein, or Gentile, or Griffiths, or Swamy et al [18,27,28] distribution functions, depending on the deviation from ideality considered.…”

Entanglement generation with deformed Barut-Girardello coherent states as input states in an unitary beam splitter

“…Deformed Peremolov and Barut-Girardello coherent states were also constructed as coherent states related to the quantum algebra U q (su(1, 1)) [39,40]. Recently, these states have attracted a lot of attention due to their possible applications in various branches of physics [39,[41][42][43]. Such states exhibit some nonclassical properties such as photon antibunching [44], sub-Poissonian photon statistics [45] and squeezing [46,47], etc (for a review see Ref.…”