Search

In this paper we present the discrete thermodynamics where the inverse temperature is not continuous but discrete. We construct the discrete analogue of Boltzmann factor based on the discrete inverse temperature lattice. We study the discrete thermodynamics related to the discrete analogue of Boltzmann factor. We also discuss the superstatistics for the discrete inverse temperature.

In this paper, we investigate the quantum fractional of the one-dimensional Klein–Gordon oscillator. By using a semiclassical approximation, the energy eigenvalues have been determined for oscillators. The obtained results show a remarkable influence of the fractional parameter $$\alpha$$ on the energy eigenvalues. By considering a unique energy spectrum, we present a simple numerical computation of the thermal properties of a defined energy spectrum of a system. The Euler–Maclaurin formula has been used to calculate the partition function and therefore the associated thermodynamics quantities. Besides this, we also calculate the eigenfunctions of our problem. The influence of the parameter $$\alpha$$ on these functions as well as the probability of density has been tested.

In this paper, we focus, at first, on the exact solutions on the one-dimensional Dirac oscillator with the energy-dependent potentials. Then, the influence of these solutions on the Shannon entropy and Fisher information, well-known in quantum information, has been studied. In this direction, we concentrated on the determination of the position and momentum information entropies for the low-lying states n=0,1,2. Some interesting features of both Fisher and Shannon densities as well as the probability densities are demonstrated. Finally, the Fisher uncertainty relation, Stam, Cramer–Rao and Bialynicki–Birula–Mycielski (BBM) inequalities have been checked and their comparison with the regarding results have been reported. We showed that the BBM inequality is still valid in the form $$S_{x}+S_{p}\ge 1+\text {ln}\pi $$ .

In this paper, we investigated the influence of energy-dependent potentials on the thermodynamic properties of the Klein-Gordon oscillator(KGO): in this way all thermal properties have been determinate via the well-know Euler-Maclaurin method. After this, we extend our study to the case of superstatistical properties of our problem in question. The probability densityf(β)followsχ2− superstatistics (=Tsallis statistics or Gamma distribution). Under the approximation of the low-energy asymptotics of superstatistics, the partition function, at first, has been calculated. This approximation leads to a universal parameterqfor any superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of the parameterq. Also, the influence of the this type of potentials on these properties, via the parameterγ, are well discussed.

In this paper, we obtain the exact solutions of Duffin-Kemmer-Petiau equation spin-1 in thepresence of the Aharonov-Bohm and Coulomb potential in the gravitational field of cosmic stringand a global monopole, we are study the DKP equation in commutative space-time, We separatedthe variables with the help of Wigner functions and the parity operator, We solved the system ofthe second order differential equation in the case of P = (−1) j+1 , but in the case of P = (−1) j wesolved the system in j = 0. The spectrum of energy in the gravitational field of cosmic string and aglobal monopole are different, and the commutation relation of the angular momentum are obviouslydifferent from Pauli criterion in the Aharonov-Bohm effect, in spin-0 and spin-1 we have the non-commutativity energy by the perturbation theory, the energy is transition from commutative tonon-commutative spac

The purpose of this study is to develop a method of calculating the vibration partition function of diatomic molecules for the Morse potential energy. After a brief introduction about the eigensolutions obtained for the problem in question, Via the Euler-Maclaurin formula, we have determined the thermal properties for four diatomics such as \text{H}_{2}, HCl, LiH, and CO. Different situation has been exposed and explained by the appropriate curves of the thermal properties for these diatomics molecules in consideration. In addition, we have shown that our method exposed to calculate these thermal properties can be used to determine these thermodynamic quantities.

In this paper, we investigate the fractional version of the one-dimensional relativistic oscillators. We apply some important definitions and properties of a new kind of fractional formalism on the Dirac oscillator (DO). By using a semiclassical approximation, the energy eigenvalues have been determined for the oscillator. The obtained results show a remarkable influence of the fractional parameter on the energy eigenvalues. By considering a unique energy spectrum, we present a simple numerical computation of the thermal properties of a defined energy spectrum of a system. the Euler–Maclaurin formula has been used to calculate the partition function and therefore the associated thermodynamics quantities. In addition, the eigensolutions of the fractional Dirac oscillator, based on the factorization method, have been determined.

In this paper, we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function, the related thermodynamic functions are derived and studied in terms of the parameters of the model. Especially, we plotted the q-deformed vibrational partition function and vibrational specific heat for some diatomic molecule systems such as \(\text {H}_{2}\), HCl, LiH, and CO. The idea of a critical temperature \(T_{C}\) is introduced in relation to the specific heat.

In this article, we test the influence of the modification of the scalar product, found in the problems of the energy-dependent potential, on the physical properties of the harmonic oscillator in one dimension. For this, we first discuss the effect of this change on the thermodynamic properties of this oscillator, and then investigate the parameters of Fisher and Shannon of quantum information. For the second problem, the dependence of these parameters with the density of state, is the main reason of our choice to study the influence of this type of potential on these properties. Finally, the well-know uncertainty relation of Cramer–Rao is well recovered.

In this paper, the problem of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator in the presence of a Coulomb potential in the cosmic string background is solved. The eigensolutions of the problem in question have been found, and the influence of the Coulomb potential in the presence of the gravitational field of cosmic string has been analyzed.

In this paper we study the one-dimension Klein-Gordon (KG) equation in the Rindler spacetime. The solutions of the wave equation in an accelerated reference frame are obtained. As a result, (i) we derive a compact expression for the energy spectrum associated in an accelerated reference, and (ii) we show that the non-inertial effect of the accelerated reference frame mimics an external potential in the Klein-Gordon equation and, moreover, allows the formation of bound states. In addition, the thermal properties of the Klein-Gordon from the partition function, have been investigated, and the effect of the accelerated reference frame parameter a on these properties has been tested. This study is extended to the case of the one-dimensional Dirac equation where the spectrum of energy is well determined and has an exact form. As a result, we will see that the behavior of the thermal quantities of the fermion particles is similar to the case of boson particles.

In this paper, we consider the thermal properties of one-dimensional Dirac in the framework of the theory of superstatistics where the probability density f ( β ) follows χ 2 − superstatistics (=Tsallis statistics or Gamma distribution). Under the approximation of the low-energy asymptotics of superstatistics, the partition function, at first, has been calculated by using both Mellin Transformation and Zeta function. This approximation leads to a universal parameter q for any superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of the parameter q . As an application, we extend this concept to the case of Graphene: the reason of this choice is due the existence of an exact mapping about the Dirac oscillator and the compound in question.

We consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

We consider a two-dimensional Dirac oscillator in the presence of magnetic field in noncommutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl-Teller potential. The eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.

In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein-Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n=0,1,2 are calculated. Some interesting features of both Fisher and Shannon densities as well as the probability densities are demonstrated., 14 figures, any comments are welcome. arXiv admin note: text overlap with arXiv:1607.02123

In this paper, we analyzed the relativistic quantum motion of a charged scalar particles in the presence of a Aharonov Bohm and Coulomb potentials in the spacetimes produced by an idealized cosmic strings and global monopoles., Comment: any comments are welcome

We will consider the relativistic Duffin-Kemmer-Petiau equation in the presence of a pseudoharmonic potential in a magnetic field in the (1+2)-dimensional space-time for spin-one particles. To derive the energy eigenvalues and corresponding eigenfunctions, the analytical Nikiforov-Uvarov Method is used and some explanatory figures are included.

We solve the Duffin–Kemmer–Petiau equation in the presence of a pseudoscalar potential step in (1 + 1) dimensions. We show that the paradox of Klein is not found for particles of spin-1, contrary to the case of the particles of spin-0 where it always persists. The absence of this paradox in the vector bosons is explained with the arguments based on effective mass.PACS Nos.: 03.65.Pm; 03.65.Ge

In this article we solved the problem of the relativistic spin-1 particle in the presence of the Aharonov–Bohm potential in two and three dimensions, while using the Duffin–Kemmer–Petiau equation. The wave functions as well as the energy spectrum, in both cases, have been obtained. The validity of the Pauli criterion in the Aharonov–Bohm effect is well discussed.

The one-dimensional thermal properties of the Kemmer oscillator have been investigated. Firstly, we have found the spectrum of energy of the oscillator in question, and then we have calculated its thermal properties. A comparison of our results with those of the Dirac oscillator has been made.

The two dimensional Kemmer oscillator under the influence of the gravitational field produced by a topology such as the cosmic string spacetime and in the presence of a uniform magnetic field as well as without magnetic field are investigated., any comments are welcome

Exact solutions of Kemmer equation for charged, massive, spin-1 particles in the Dirac oscillator potential have been found. The eigensolutions of this potential have been calculated and discussed in both natural and unnatural parities.

Dans ce présent article, nous discutons l'interaction de la particule de spin 0 avec un potentiel d'Aharonov–Bohm à deux et trois dimensions par l'application de l'équation de Duffin–Kemmer–Petiau. Le spectre d'énergie et sa dépendance avec l'intensité du potentiel d'Aharonov–Bohm sont analysés.PACS Nos : 03.65.Pm, 03.65.Ge

We have investigated the Duffin–Kemmer–Petiau (DKP) equation, with equally vector and scalar potentials for the general deformed Morse potential, then we obtained creation and annihilation operators and showed that these operators satisfied the commutation relation of the [Formula: see text]group. The Casimir operator defined for Laguerre polynomials.

We study the (2+1)-dimensional Dirac oscillator in the presence of an external uniform magnetic field in noncommutative space. Then, we obtain the energy spectrum. In addition, we consider the statistical properties of the system.

The state of the Yb3+ ion of the ytterbium iron garnet (Yb3Fe5O12) is suitable for the development of theoretical models with rather good approximations. Using the theory of two-level paramagnetic ions, the total and magnetic specific heat at low temperatures has been calculated. The influence of tensors g and G on the specific heat of YbIG has been examined. A comparison has been made of our results and those obtained with a model based on of the approximation of Weiss Molecular-Field (WMF) and experimental data.

In the language of creation and annihilation operators, we study a relativistic spin- $$\tfrac{1} {2}$$ fermion subject to a Dirac oscillator (DO) coupling and a constant magnetic field in both commutative and non-commutative (NC) spaces. All dynamical physical variables, in a two-dimensional complex formalism, are expressed in terms of the creation and annihilation operators via a z , $$\bar a_z$$ and a z , $$\bar a_z$$ in the commutative space, and d z , $$\bar d_z$$ and d z , $$\bar d_z$$ in the NC space. The eigensolutions of our problem have been determinated, and the exact connection with both Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) models has been established. In addition, we revealed the existence of the quantum phase transition in both commutative and NC spaces. The thermal properties of the Dirac oscillator under a magnetic field, calculated from the partition function, have been investigated, and the effect of the non-commutative parameters on these properties has been tested.

The effect of the minimal length on the thermal properties of a Dirac oscillator is considered. The canonical partition function is well determined by using the method based on the Epstein Zeta function. Through this function, all thermodynamics properties, such as the free energy, the total energy, the entropy, and the specific heat, have been determined. Moreover, this study leads to a minimal length in the interval 10 16 �0 = 1 m2 c2. We show that this condition is obtained directly through the properties � = ~

In this paper, we show, by using the approach of effective mass, that the model of a two-dimensional Dirac oscillator can be used to describe the thermodynamic properties of graphene under a uniform magnetic field. All thermodynamic quantities of graphene, such as the free energy, the mean energy, the entropy and the specific heat, have been found by using an approach based on the zeta function.

We study the relativistic spin-zero bosons influenced by the Klein-Gordon oscillator and an external magnetic field in noncommutative formulation. The problem is considered in two dimensions and is solved in an exact analytical manner. Having found the spectrum of the system, the statistical properties of an N-boson system are reported.

In the paper of Ref. 1, and according the eigensolutions of the case of spin-1 particles, we note that (i) first, when we put ω = 0 in Eq. (25) of Ref. 1, the well-known relation of a free particles E2 = c2p2 + m2c4, is not well established, and (ii) second, the form of the spectrum of energy (Eqs. (37) and (41) in Ref. 1) led to the possibility of the existence of a complex eigenvalues.

We study S-wave solutions of the Duffin-Kemmer-Petiau (DKP) equation in the presence of a hyperbolical potential in (1+3)-dimensional space-time for spin-one particles. The exact analytical Nikiforov-Uvarov (NU) method is used in the calculations to obtain the eigenfunctions and the corresponding eigenvalues. Some figures and numerical values are included to give a better insight to the solutions.

The correct energy profile of the one-dimensional Klein–Gordon oscillator, discussed by Rao and Kagali (2008 Phys. Scr. 77 015003), is obtained here by the prescription of Mirza and Mohadesi (2004 Commun. Theor. Phys. 42 6646–68) and Mirza et al (2011 Commun. Theor. Phys. 55 405–9). Using this prescription, the solutions are obtained in the framework of a method based on the usual annihilation and creation operators.

Two-dimensional eigenfunctions and eigenvalues of massive spin-1 particles in the presence of the Dirac oscillator have been found by using the Kemmer equation. We derive a complete analytical solution of the system, describing in detail the energy spectrum and associated eigensolutions by using the formalism of the chiral creation–annihilation operators.

The one-dimensional eigenfunctions and the eigenvalues of massive spin-0 and spin-1 particles have been found by using the Duffin–Kemmer–Petiau equation. Following Greiner [Quantum Mechanics: An introduction, 4th ed. (Springer-verlag, Berlin, 2001)], we have shown that the eigensolutions in both cases are decoupled in two sets.