Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Theoretical Physics

Superstatistics of Modified Rosen-Morse Potential with Dirac Delta and Uniform Distributions

U. S. Okorie, A. N. Ikot, Gaotsiwe Joel Rampho, R. Sever

Published Oct 1, 2019• 11 citations
Publisher

Abstract

Abstract We discuss the thermodynamic properties of a modified Rosen-Morse potential using the q -deformed superstatistics approaches. We obtain the partition function with the help of the generalized Boltzmann factor from the modified Dirac delta distribution and uniform distribution. Other thermodynamic function is obtained for the superstatistics of the two distributions considered. We also discuss our results graphically and obtain the ordinary statistical quantities when the deformation parameter tends to zero.

DOI
10.1088/0253-6102/71/10/1246

Related papers

Superstatistics of two electrons quantum dot

Sepideh Sargolzaeipor, HASSAN HASSANABADI, Won Sang Chung

In this paper, we discussed the Schrödinger equation in the presence of the harmonic two electrons interaction for the parabolic quantum dot and the energy spectrum by an analytical method is obtained, then the effective Boltzmann factor in a deformed formalism for modified Dirac delta and uniform distributions are derived. We make use of the superstatistics for the two distributions in physics and the thermodynamic properties of the system are calculated. Ordinary results are recovered for the vanishing deformed parameter. Furthermore, the effect of all parameters in the problems are calculated and shown graphically.

Modern Physics Letters A•Jan 16, 2019•15 citations

Superstatistics properties of q-deformed Morse potential in one dimension

Hassanabadi, H., Sargolzaeipor, S., Chung, W.S.

In this paper, after introducing superstatistics in quantum mechanics, first, the Schrödinger equation in one-dimensional in the presence of q-deformed Morse potential is derived. We use an analytical methodology to calculate the energy eigenvalues. Then the thermodynamic properties of the system are calculated. Furthermore, we report effects of all parameters in the problems on the thermodynamic quantities.

•Jan 1, 2018•0 citations

Analytical Solution of Dirac Equation for q-Deformed Hyperbolic Manning-Rosen Potential in D Dimensions using SUSY QM and its Thermodynamics'Application

C. Cari, Suparmi Suparmi, Mohtar Yunianto +1 more

The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function.

Journal of Physics Conference Series•Aug 1, 2016•3 citations

On Quantum Superstatistics and the Critical Behavior of Nonextensive Ideal Bose Gases

Octavio Obregón, José Luis López, Marco Ortega-Cruz

We explore some important consequences of the quantum ideal Bose gas, the properties of which are described by a non-extensive entropy. We consider in particular two entropies that depend only on the probability. These entropies are defined in the framework of superstatistics, and in this context, such entropies arise when a system is exposed to non-equilibrium conditions, whose general effects can be described by a generalized Boltzmann factor and correspondingly by a generalized probability distribution defining a different statistics. We generalize the usual statistics to their quantum counterparts, and we will focus on the properties of the corresponding generalized quantum ideal Bose gas. The most important consequence of the generalized Bose gas is that the critical temperature predicted for the condensation changes in comparison with the usual quantum Bose gas. Conceptual differences arise when comparing our results with the ones previously reported regarding the q-generalized Bose–Einstein condensation. As the entropies analyzed here only depend on the probability, our results cannot be adjusted by any parameter. Even though these results are close to those of non-extensive statistical mechanics for q ∼ 1 , they differ and cannot be matched for any q.

Entropy•Oct 9, 2018•6 citations

Exact analytic solutions of the Schrödinger equations for some modified q-deformed potentials

M. Sebawe Abdalla, Hichem Eleuch

In this paper, we introduce the exact solution for the wave function in the presence of potential energy, consisting of combination between q-deformed hyperbolic and exponential function with different argument. The functions we have used in the present communication can be regarded as a generalization of the Arai q-deformed function (modified q-deformed Morse potential). In this context, we have restricted our discussion for some particular cases of the q-deformed hyperbolic functions. This is due to the difficulty for dealing with most of the arguments included in the potential functions. For the most particular cases, the energy eigenfunctions are obtained, and the behavior is also discussed. It has been shown that the wave functions are sensitive to the variation in the value of q-deformed parameter as well as the strength of the potential parameter λ. Furthermore, the energy eigenvalues are also considered for some particular cases where the argument of the exponential function plays a strong role effecting its value.

Journal of Applied Physics•Jun 18, 2014•23 citations

Thermostatistic properties of aq-deformed ideal Fermi gas with a general energy spectrum

Shukuan Cai, Guozhen Su, Jincan Chen

The thermostatistic problems of a q -deformed ideal Fermi gas in any dimensional space and with a general energy spectrum are studied, based on the q -deformed Fermi–Dirac distribution. The effects of the deformation parameter q on the properties of the system are revealed. It is shown that q -deformation results in some novel characteristics different from those of an ordinary system. Besides, it is found that the effects of the q -deformation on the properties of the Fermi systems are very different for different dimensional spaces and different energy spectrums.

Journal of Physics A Mathematical and Theoretical•Aug 29, 2007•30 citations
Abstract We discuss the thermodynamic properties of a modified Rosen-Morse potential using the q -deformed superstatistics approaches. We obtain the partition function with the help of the generalized Boltzmann factor from the modified Dirac delta distribution and uniform distribution. Other thermodynamic function is obtained for the superstatistics of the two distributions considered. We also discuss our results graphically and obtain the ordinary statistical quantities when the deformation parameter tends to zero.
In this paper, we discussed the Schrödinger equation in the presence of the harmonic two electrons interaction for the parabolic quantum dot and the energy spectrum by an analytical method is obtained, then the effective Boltzmann factor in a deformed formalism for modified Dirac delta and uniform distributions are derived. We make use of the superstatistics for the two distributions in physics and the thermodynamic properties of the system are calculated. Ordinary results are recovered for the vanishing deformed parameter. Furthermore, the effect of all parameters in the problems are calculated and shown graphically.
The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function.
We explore some important consequences of the quantum ideal Bose gas, the properties of which are described by a non-extensive entropy. We consider in particular two entropies that depend only on the probability. These entropies are defined in the framework of superstatistics, and in this context, such entropies arise when a system is exposed to non-equilibrium conditions, whose general effects can be described by a generalized Boltzmann factor and correspondingly by a generalized probability distribution defining a different statistics. We generalize the usual statistics to their quantum counterparts, and we will focus on the properties of the corresponding generalized quantum ideal Bose gas. The most important consequence of the generalized Bose gas is that the critical temperature predicted for the condensation changes in comparison with the usual quantum Bose gas. Conceptual differences arise when comparing our results with the ones previously reported regarding the q-generalized Bose–Einstein condensation. As the entropies analyzed here only depend on the probability, our results cannot be adjusted by any parameter. Even though these results are close to those of non-extensive statistical mechanics for q ∼ 1 , they differ and cannot be matched for any q.
In this paper, we introduce the exact solution for the wave function in the presence of potential energy, consisting of combination between q-deformed hyperbolic and exponential function with different argument. The functions we have used in the present communication can be regarded as a generalization of the Arai q-deformed function (modified q-deformed Morse potential). In this context, we have restricted our discussion for some particular cases of the q-deformed hyperbolic functions. This is due to the difficulty for dealing with most of the arguments included in the potential functions. For the most particular cases, the energy eigenfunctions are obtained, and the behavior is also discussed. It has been shown that the wave functions are sensitive to the variation in the value of q-deformed parameter as well as the strength of the potential parameter λ. Furthermore, the energy eigenvalues are also considered for some particular cases where the argument of the exponential function plays a strong role effecting its value.
The thermostatistic problems of a q -deformed ideal Fermi gas in any dimensional space and with a general energy spectrum are studied, based on the q -deformed Fermi–Dirac distribution. The effects of the deformation parameter q on the properties of the system are revealed. It is shown that q -deformation results in some novel characteristics different from those of an ordinary system. Besides, it is found that the effects of the q -deformation on the properties of the Fermi systems are very different for different dimensional spaces and different energy spectrums.