Abstract Based on the framework established in a recent work (Ubriaco in Physica A 414:128, 2014), wherein a generalized bosonic model was formulated using the Dunkl operator formalism (DOF), we extend this approach to its different applications with introducing a statistical distribution—termed the Dunkl-deformed Bose–Einstein (DDBE) distribution—constructed by generalizing the usual Bose–Einstein distribution through the DOF. In this framework, we study further general thermodynamical and statistical properties of a gas model of the Dunkl-deformed bosons obeying the DDBE statistics. Emphasis is given to a careful analysis on the conditions under which the Bose–Einstein-like condensation would occur in the present Dunkl-deformed boson gas. It is shown that the critical temperature for such a system is higher than that of the usual (undeformed) Bose gas for values of the model deformation parameter $\theta$ θ in the range $\theta > 0$ θ > 0 . As another application of the DDBE statistics, we investigate the thermostatistics of the Dunkl-deformed Debye solid and the effects of the deformation parameter $\theta$ θ on the high- and low-temperature behavior of the model specific heat are discussed. Our results obtained in this study could provide much physical insight for approaching not only in the treatment of interacting bosons theories including collective excitations, but also in the condensation characteristics of quantum systems beyond the standard formalism.Abstract Based on the framework established in a recent work (Ubriaco in Physica A 414:128, 2014), wherein a generalized bosonic model was formulated using the Dunkl operator formalism (DOF), we extend this approach to its different applications with introducing a statistical distribution—termed the Dunkl-deformed Bose–Einstein (DDBE) distribution—constructed by generalizing the usual Bose–Einstein distribution through the DOF. In this framework, we study further general thermodynamical and statistical properties of a gas model of the Dunkl-deformed bosons obeying the DDBE statistics. Emphasis is given to a careful analysis on the conditions under which the Bose–Einstein-like condensation would occur in the present Dunkl-deformed boson gas. It is shown that the critical temperature for such a system is higher than that of the usual (undeformed) Bose gas for values of the model deformation parameter $$\theta$$ θ in the range $$\theta > 0$$ θ > 0 . As another application of the DDBE statistics, we investigate the thermostatistics of the Dunkl-deformed Debye solid and the effects of the deformation parameter $$\theta$$ θ on the high- and low-temperature behavior of the model specific heat are discussed. Our results obtained in this study could provide much physical insight for approaching not only in the treatment of interacting bosons theories including collective excitations, but also in the condensation characteristics of quantum systems beyond the standard formalism.

The European Physical Journal PlusMar 16, 20262 citations

q-deformed Bose statistics and the Gross–Pitaevskii equation

Mahnaz Maleki, Zahra Ebadi, Hosein Mohammadzadeh

In continuation of our earlier work on the nonextensive form of the Gross–Pitaevskii equation (GPE) [M. Maleki, H. Mohammadzadeh and Z. Ebadi, Int. J. Geom. Methods Mod. Phys. 20 (2023) 2350216], we now delve into its [Formula: see text]-deformed counterpart. GPE is a type of nonlinear partial differential equation that is specifically designed to describe the behavior of a group of particles with Bose–Einstein statistics, such as atoms in a superfluid or a Bose–Einstein condensate (BEC). In some systems, the standard Bose–Einstein or Fermi–Dirac statistics may not apply, and generalized statistics may be needed to describe the behavior of the particles. Therefore in this paper, we investigate the dynamics of a system with particle obeying [Formula: see text]-deformed statistics described by the [Formula: see text]-deformed GPE. First, we use the oscillator algebra and [Formula: see text]-calculus to obtain the well-known Schrödinger equation. By selecting an appropriate Hamiltonian for the condensate phase and minimizing the free energy, we derive the [Formula: see text]-deformed time-independent GPE.In continuation of our earlier work on the nonextensive form of the Gross–Pitaevskii equation (GPE) [M. Maleki, H. Mohammadzadeh and Z. Ebadi, Int. J. Geom. Methods Mod. Phys. 20 (2023) 2350216], we now delve into its [Formula: see text]-deformed counterpart. GPE is a type of nonlinear partial differential equation that is specifically designed to describe the behavior of a group of particles with Bose–Einstein statistics, such as atoms in a superfluid or a Bose–Einstein condensate (BEC). In some systems, the standard Bose–Einstein or Fermi–Dirac statistics may not apply, and generalized statistics may be needed to describe the behavior of the particles. Therefore in this paper, we investigate the dynamics of a system with particle obeying [Formula: see text]-deformed statistics described by the [Formula: see text]-deformed GPE. First, we use the oscillator algebra and [Formula: see text]-calculus to obtain the well-known Schrödinger equation. By selecting an appropriate Hamiltonian for the condensate phase and minimizing the free energy, we derive the [Formula: see text]-deformed time-independent GPE.

International Journal of Geometric Methods in Modern PhysicsDec 17, 20232 citations

q-Deformed Gross Pitaevskii Equation

Mahnaz Maleki, Hosein Mohammadzadeh

We derive the Gross Pitaevskii equation (GPE) for condensate of bosons obeying deformed statistics under external potential and inter-particle interaction. First, we obtain the well-known Schrodinger equation. Using a suitable Hamiltonian for condensate phase and minimizing the free energy of the system, we find out the $q$ - deformed GPE. Thus, at very low temperature, where the dynamics of excited-occupation level can be neglected, the dynamics of a deformed statistics system can be described by the GPE, similar to the Bose-Einstein condensate.We derive the Gross Pitaevskii equation (GPE) for condensate of bosons obeying deformed statistics under external potential and inter-particle interaction. First, we obtain the well-known Schrodinger equation. Using a suitable Hamiltonian for condensate phase and minimizing the free energy of the system, we find out the $q$- deformed GPE. Thus, at very low temperature, where the dynamics of excited-occupation level can be neglected, the dynamics of a deformed statistics system can be described by the GPE, similar to the Bose-Einstein condensate.

arXiv:2302.04571Feb 9, 20230 citations

\theta

θ in the range

\theta > 0

θ > 0 . As another application of the DDBE statistics, we investigate the thermostatistics of the Dunkl-deformed Debye solid and the effects of the deformation parameter

\theta

θ on the high- and low-temperature behavior of the model specific heat are discussed. Our results obtained in this study could provide much physical insight for approaching not only in the treatment of interacting bosons theories including collective excitations, but also in the condensation characteristics of quantum systems beyond the standard formalism.

q

- deformed GPE. Thus, at very low temperature, where the dynamics of excited-occupation level can be neglected, the dynamics of a deformed statistics system can be described by the GPE, similar to the Bose-Einstein condensate.