Geodesic
Statistical properties of the one-dimensional Dirac oscillator in Rindler space–time
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 1, pp. 220-232 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the spin-$1/2$ relativistic fermions influenced by the Dirac oscillator in Rindler's space–time. The energy eigenvalues of this oscillator enable us to calculate the thermodynamic properties of this oscillator by using the Hurwitz zeta function via the Mellin transformation. The effect of the geometry of space–time on these properties is studied.
Keywords: Dirac oscillator, Rindler space–time, partition function, Hurwitz zeta function. 
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T. I. Rouabhia; A. Boumali. Statistical properties of the one-dimensional Dirac oscillator in Rindler space–time. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 1, pp. 220-232. http://geodesic.mathdoc.fr/item/TMF_2023_217_1_a11/

[1] W.-Y. Tsai, A. Yildiz, “Motion of charged particles in a homogeneous magnetic field”, Phys. Rev. D., 4:12 (1971), 3643–3648 ; T. Goldman, W.-Y. Tsai, “Motion of charged particles in a homogeneous magnetic field. II”, 3648–3651 | DOI | DOI

[2] L. D. Krase, Pao Lu, R. H. Good, Jr., “Stationary states of a spin-1 particle in a constant magnetic field”, Phys. Rev. D., 3:6 (1971), 1275–1279 | DOI

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

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

[5] C. Quesne, M. Moshinsky, “Symmetry Lie algebra of the Dirac oscillator”, J. Phys. A: Math. Gen, 23:12 (1990), 2263–2272 | DOI | MR

[6] R. P. Martínez-y-Romero, A. L. Salas-Brito, “Conformal invariance in a Dirac oscillator”, J. Math. Phys., 33:5 (1992), 1831–1836 | DOI | MR

[7] M. Moreno, A. Zentella, “Covariance, CPT and the Foldy–Wouthuysen transformation for the Dirac oscillator”, J. Phys. A: Math. Gen., 22:17 (1989), L821–L825 | DOI | MR

[8] W. Rindler, Essential Relativity: Special, General, and Cosmological, Springer, Berlin, 1977 | DOI | MR

[9] W. Rindler, “General Relativity”, Book review, Science, 230:4731 (1985), 1268–1269 | DOI

[10] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 2, Teoriya polya, Fizmatlit, M., 1988 | MR

[11] L. Parker, “One-electron atom in curved space-time”, Phys. Rev. Lett., 44:23 (1980), 1559–1562 ; “One-electron atom as a probe of spacetime curvature”, Phys. Rev. D, 22:8 (1980), 1922–1934 ; “Self-forces and atoms in gravitational fields”, 24:2 (1981), 535–537 ; “The atom as a probe of curved space-time”, Gen. Relat. Gravit., 13:4 (1981), 307–311 | DOI | MR | DOI | DOI | DOI

[12] L. C. N. Santos, C. C. Barros, Jr., “Dirac equation and the Melvin metric”, Eur. Phys. J. C, 76:10 (2016), 560, 7 pp. ; “Scalar bosons under the influence of noninertial effects in the cosmic string spacetime”, 77:3 (2017), 186, 7 pp. | DOI | DOI

[13] 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

[14] M.-A. Dariescu, C. Dariescu, “Persistent currents and critical magnetic field in planar dynamics of charged bosons”, J. Phys.: Condens. Matter, 19:25 (2007), 256203, 9 pp. | DOI

[15] M.-A. Dariescu, C. Dariescu, “Finite temperature analysis of quantum Hall-type behavior of charged bosons”, Chaos Solitons Fractals, 33:3 (2007), 776–781 | DOI

[16] A. Boumali, “The one-dimensional thermal properties for the relativistic harmonic oscillators”, Electronic J. Theor. Phys., 12:32 (2015), 121–130, arXiv: 1409.6205

[17] E. Elizalde, S. D. Odintsov, A. Romeo, A. A. Bytsenko, S. Zerbini, Zeta Regularization Techniques with Applications, World Sci., Singapore, 1994 ; E. Elizalde, Ten Physical Applications of Spectral Zeta Functions, Lecture Notes in Physics, 855, Springer, Berlin, 2012 | DOI | MR | DOI | MR

[18] L. C. N. Santos, C. E. Mota, C. C. Barros, Jr., L. B. Castro, V. B. Bezerra, “Quantum dynamics of scalar particles in the space-time of a cosmic string in the context of gravity's rainbow”, Ann. Physics, 421 (2020), 168276, 14 pp. | DOI | MR

[19] R. Szmytkowski, M. Gruchowski, “Completeness of the Dirac oscillator eigenfunctions”, J. Phys. A: Math. Gen., 34:23 (2001), 4991–4997 | DOI | MR

[20] A. Boumali, T. I. Rouabhia, “The thermal properties of the one-dimensional boson particles in Rindler spacetime”, Phys. Lett. A, 385 (2021), 126985, 8 pp. | DOI | MR

[21] V. Mukhanov, S. Winitzk, Introduction to Quantum Effects in Gravity, Cambridge Univ. Press, Cambridge, 2007 | MR

[22] M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics, Institute of Physics, Bristol, 2003 | MR | Zbl

[23] R. A. Bertlmann, Anomalies in Quantum Field Theory, International Series of Monographs on Physics, Oxford Univ. Press, New York, 2000 | DOI

[24] S. K. Moayedi, F. Darabi, “Exact solutions of Dirac equation on a 2D gravitational background”, Phys. Lett. A, 322:3–4 (2004), 173–178 | DOI | MR

[25] R. Jackiw, C. Rebbi, “Solitons with fermion number $1/2$”, Phys. Rev. D, 13:12 (1976), 3398–3409 | DOI | MR

[26] L. C. N. Santos, C. C. Barros, “Fermions in the Rindler spacetime”, Internat. J. Geom. Methods Modern Phys., 16:9 (2019), 1950140, 10 pp. | DOI | MR

[27] S. Flügge, “Practical Quantum Mechanics”, Book rewiews, Amer. J. Phys., 41:1 (1973), 140 | DOI | MR

[28] S. Flügge, Practical Quantum Mechanics, Classics in Mathematics, Springer, Berlin, Heidelberg, 2012 | DOI | MR

[29] J. Carvalho, C. Furtado, F. Moraes, “Dirac oscillator interacting with a topological defect”, Phys. Rev. A, 84:3 (2011), 032109, 6 pp. | DOI

[30] A. Boumali, N. Messai, “Klein–Gordon oscillator under a uniform magnetic field in cosmic string space-time”, Can. J. Phys., 92:11 (2014), 1460–1463 | DOI

[31] A. Boumali, A. Hafdallah, A. Toumi, “Comment on ‘Energy profile of the one-dimensional Klein–Gordon oscillator’ ”, Phys. Scr., 84:3 (2011), 037001, 3 pp. | DOI

[32] A. M. Frassino, D. Marinelli, O. Panella, P. Roy, “Thermodynamics of quantum phase transitions of a Dirac oscillator in a homogenous magnetic field”, J. Phys. A: Math. Theor, 53:18 (2020), 185204, 19 pp. | DOI | MR

[33] A. Boumali, F. Serdouk, S. Dilmi, “Superstatistical properties of the one-dimensional Dirac oscillator”, Phys. A, 533 (2020), 124207, 13 pp. | DOI | MR

[34] J. D. Castano-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

[35] M. Moreno, R. Martínez, A. Zentella, “Supersymmetry, Foldy–Wouthuysen transformation and stability of the Dirac sea”, Modern Phys. Lett. A., 5:12 (1990), 949–954 | DOI | MR

[36] L. L. Foldy, S. A. Wouthuysen, “On the Dirac theory of spin 1/2 particles and its non-relativistic limit”, Phys. Rev., 78:1 (1950), 29–36 | DOI

[37] N. M. Myers, O. Abah, S. Deffner, “Quantum Otto engines at relativistic energies”, New. J. Phys., 23 (2021), 105001, 16 pp. | DOI | MR

[38] 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, 18 pp. | DOI