Geodesic
Superstatistical properties of the Dirac oscillator with gamma, lognormal, and F distributions
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 163-180
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We explore the thermal characteristics of fermionic fields with a nonminimal coupling in one, two, and three dimensions using the framework of superstatistics theory. We consider three distinct distributions: the gamma distribution, the lognormal distribution, and the F distribution. Each of these distributions is governed by a specific probability density function. To calculate the partition function, we use the Euler–Maclaurin formula, specifically in the low-energy asymptotic approximation of superstatistics. This calculation takes the remainder term into consideration. In each scenario, using the derived partition functions, we analyze the variations in entropy and specific heat with varying temperatures and the universal parameter denoted as $q$. In general, we observe that increasing the value of $q$ enhances all the curves. Additionally, we note that entropy values tend to increase as the temperature decreases, and tend to decrease as the parameter $q$ increases.
Keywords: thermal properties, Dirac oscillator, superstatistics, Euler–Maclaurin formula. 
@article{TMF_2024_219_1_a10,
     author = {S. Siouane and A. Boumali and A. Guvendi},
     title = {Superstatistical properties of {the~Dirac} oscillator with gamma, lognormal, and {F} distributions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {163--180},
     year = {2024},
     volume = {219},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a10/}
}
TY  - JOUR
AU  - S. Siouane
AU  - A. Boumali
AU  - A. Guvendi
TI  - Superstatistical properties of the Dirac oscillator with gamma, lognormal, and F distributions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2024
SP  - 163
EP  - 180
VL  - 219
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a10/
LA  - ru
ID  - TMF_2024_219_1_a10
ER  - 
%0 Journal Article
%A S. Siouane
%A A. Boumali
%A A. Guvendi
%T Superstatistical properties of the Dirac oscillator with gamma, lognormal, and F distributions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2024
%P 163-180
%V 219
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a10/
%G ru
%F TMF_2024_219_1_a10
S. Siouane; A. Boumali; A. Guvendi. Superstatistical properties of the Dirac oscillator with gamma, lognormal, and F distributions. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 163-180. http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a10/

[1] M. Moshinsky, A. Szczepaniak, “The Dirac oscillator”, J. Phys. A: Math. Gen., 22:17 (1989), L817–L819 | DOI | MR

[2] A. Boumali, “On the eigensolutions of the one-dmensional Kemmer oscillator”, Turkish J. Phys., 31:6 (2007), 307–316

[3] D. Itô, K. Mori, E. Carriere, “An example of dynamical systems with linear trajectory”, Nuovo Cimento A, 51:4 (1967), 1119–1121 | DOI

[4] A. Guvendi, “Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction”, Eur. Phys. J. C, 81:2 (2021), 100, 7 pp. | DOI

[5] A. Bermudez, M. A. Martin-Delgado, E. Solano, “Exact mapping of the $2+1$ Dirac oscillator onto the Jaynes–Cummings model: Ion-trap experimental proposal”, Phys. Rev. A, 76:4 (2007), 041801, 4 pp. | DOI

[6] C. Beck, E. G. D. Cohen, “Superstatistics”, Phys. A, 322:1–4 (2003), 267–275 | DOI | MR

[7] E. G. D. Cohen, “Superstatistics”, Phys. D, 193:1–4 (2004), 35–52 | DOI | MR

[8] A. Guvendi, A. Boumali, “Superstatistical properties of a fermion-antifermion pair interacting via Dirac oscillator coupling in one-dimension”, Eur. Phys. J. Plus, 136:11 (2021), 1098, 18 pp. | DOI

[9] C. Beck, “Generalized statistical mechanics for superstatistical systems”, Philos. Trans. R. Soc. London Ser. A, 369:1935 (2011), 453–465 | DOI | MR

[10] T. Yamano, “Thermodynamical and informational structure of superstatistics”, Prog. Theor. Phys. Suppl., 162 (2006), 87–96 | DOI | MR

[11] A. Boumali, F. Serdouk, S. Dilmi, “Superstatistical properties of the one-dimensional Dirac oscillator”, Phys. A, 553 (2020), 124207, 13 pp. | DOI | MR

[12] M. Labidi, A. Boumali, A. Ndem Ikot, “Superstatistics of the one-dimensional Klein–Gordon oscillator with energy–dependent potentials”, Rev. Mexicana Fís., 66:5 (2020), 671–682 | DOI | MR

[13] C. Tsallis, “Nonextensive statistical mechanics and thermodynamics: Historical background and present status”, Nonextensive Statistical Mechanics and Its Applications, Lecture Notes in Physics, 560, eds. S. Abe, Y. Okamoto, Springer, Berlin, 2001 | DOI

[14] C. Tsallis, Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World, Springer, New York, 2009 | DOI

[15] H. Touchette, C. Beck, “Asymptotics of superstatistics”, Phys. Rev. E, 71:1 (2005), 016131, 6 pp. | DOI

[16] C. Tsallis, A. M. C. Souza, “Constructing a statistical mechanics for Beck–Cohen superstatistics”, Phys. Rev. E, 67:2 (2003), 026106, 5 pp. | DOI

[17] S. Sargolzaeipor, H. Hassanabadi, W. S. Chung, “$q$-deformed superstatistics of the Schrödinger equation in commutative and noncommutative spaces with magnetic field”, Eur. Phys. J. Plus, 133:1 (2018), 5, 11 pp. | DOI

[18] W. S. Chung, H. Hassanabadi, “Superstatistics with $q$-deformed Dirac delta distribution and interacting gas model”, Phys. A, 516 (2019), 496–501 | DOI | MR

[19] W. S. Chung, H. Hassanabadi, “Fermi energy in the $q$-deformed quantum mechanics”, Mod. Phys. Lett. A, 35:11 (2020), 2050074, 15 pp. | DOI | Zbl

[20] A. Ayala, M. Hentschinski, L. A. Hernández, M. Loewe, R. Zamora, “Superstatistics and the effective QCD phase diagram”, Phys. Rev. D, 98:11 (2018), 114002, 8 pp. | DOI | MR

[21] P. O. Amadi, C. O. Edet, U. S. Okorie, G. T. Osobonye, G. J. Rampho, A. N. Ikot, Superstatistics of the screened Kratzer potential with modified Dirac delta and uniform distributions, arXiv: 2001.10496

[22] J. D. Castano-Yepes, C. F. Ramirez-Gutierrez, “Superstatistics and quantum entanglement in the isotropic spin-1/2 $XX$ dimer from a nonadditive thermodynamics perspective”, Phys. Rev. E, 104:2 (2021), 024139, 7y pp. | DOI | MR

[23] J. D. Castaño-Yepes, D. A. Amor-Quiroz, “Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin-orbit interaction”, Phys. A, 548 (2020), 123871, 11 pp. | DOI | MR

[24] J. D. Castaño-Yepes, I. A. Lujan-Cabrera, C. F. Ramirez-Gutierrez, “Comments on Superstatistical properties of the one-dimensional Dirac oscillator by Abdelmalek Boumali et al.”, Phys. A, 580 (2021), 125206, 7 pp. | DOI | MR

[25] J. Fuentes, O. Obregón, A superstatistical formulation of complexity measures, arXiv: 2101.09147

[26] C. Beck, “Superstatistics in high-energy physics”, Eur. Phys. J. A, 40:3 (2009), 267–273 | DOI

[27] A. Boumali, “The one-dimensional thermal properties for the relativistic harmonic oscillators”, Electronic J. Theor. Phys., 12:32 (2015), 1–10, arXiv: 1409.6205

[28] A. Boumali, H. Hassanabadi, “The thermal properties of a two-dimensional Dirac oscillator under an external magnetic field”, Eur. Phys. J. Plus, 128:10 (2013), 124, 13 pp. | DOI

[29] M. Moshinsky, Yu. F. Smirnov, The Harmonic Oscillator in Modern Physics, Contemporary Concepts in Physics, 9, Harwood Academic Publ., Amsterdam, 1996 | Zbl

[30] M. H. Pacheco, R. V. Maluf, C. A. S. Almeida, R. R. Landim, “Three-dimensional Dirac oscillator in a thermal bath”, Europhys. Lett., 108:1 (2014), 10005, arXiv: 1406.5114 | DOI

[31] V. Santos, R. V. Maluf, C. A. S. Almeida, “Ann. Phys.”, Thermodynamical properties of graphene in noncommutative phase-space, 349 (2014), 402–410 | DOI

[32] A. Boumali, “Thermodynamic properties of the graphene in a magnetic field via the two-dimensional Dirac oscillator”, Phys. Scr., 90:4 (2015), 045702 | DOI

[33] M. H. Pacheco, R. R. Landim, C. A. S. Almeida, “One-dimensional Dirac oscillator in a thermal bath”, Phys. Lett. A, 311:2–3 (2003), 93–96 | DOI | MR

[34] V. G. Kats, P. Chen, Kvantovyi analiz, MTsNMO, M., 2005 | DOI | MR

[35] R. Aski, P. Roi, Dzh. Endryus, Spetsialnye funktsii, MTsNMO, M., 2013 | MR

[36] P. Erdős, S. S. Wagstaff, Jr., “The fractional parts of the Bernoulli numbers”, Illinois J. Math., 24:1 (1980), 104–112 | DOI | MR

[37] D. Elliot, “The Euler–Maclaurin formula revisited”, ANZIAM J., 40 (1998), E27–E76 | DOI