The quantum and Klein-Gordon oscillators in a non-commutative complex space and the thermodynamic functions. (English) Zbl 1298.81090
Summary: In this work we study the quantum and Klein-Gordon oscillators in a non-commutative complex space. We show that a particle described by such oscillators behaves similarly as an electron with spin in a commutative space in an external uniform magnetic field. Therefore the wave-function \(\psi(z,\bar z)\) takes values in \(C^4\), spin up, spin down, particle, antiparticle, a result which is obtained by the Dirac theory. We obtain the energy levels by exact solutions. We also derive the thermodynamic functions associated to the partition function, and show that the non-commutativity effects are manifested in energy at the high temperature limit.
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81Q60 | Supersymmetry and quantum mechanics |
References:
| [1] | Wheeler, J.A.: Geometrodynamics. Academic Press, New York (1962) · Zbl 0124.22207 |
| [2] | Witten, L.: Gravitation: An Introduction to Current Research. Wiley, New York (1962) · Zbl 0115.43103 |
| [3] | Heisenberg, W.; Pauli, W. (ed.), Letter from Heisenberg to Peierls (1985), Berlin |
| [4] | Snyder, H.S.: Quantized space-time. Phys. Rev. 71, 38 (1947) · Zbl 0035.13101 · doi:10.1103/PhysRev.71.38 |
| [5] | Manin, Y.I.: Multiparametric quantum deformation of the general linear supergroup. Commun. Math. Phys. 123, 163 (1989) · Zbl 0673.16004 · doi:10.1007/BF01244022 |
| [6] | Wess, J.: In: q-Deformed Heisenberg Algebras. Lecture Notes in Physics, vol. 543. Springer, Berlin (2000). arXiv:math-ph/9910013 · Zbl 1044.81634 |
| [7] | Aschieri, P.; Blohmann, C.; Dimitrijevic, M.; Meyer, F.; Schupp, P.; Wess, J., No article title, Class. Quantum Gravity, 22, 3511 (2005) · Zbl 1129.83011 |
| [8] | Nair, V. P.; Polychronakos, A. P., No article title, Phys. Lett. B, 505, 267 (2001) · Zbl 0977.81046 · doi:10.1016/S0370-2693(01)00339-2 |
| [9] | Ghosh, P. K., No article title, Eur. Phys. J. C, 42, 355 (2005) · Zbl 1191.81121 · doi:10.1140/epjc/s2005-02275-0 |
| [10] | Alvarez, P. D.; Gomis, J.; Kamimura, K.; Plyushchay, M. S., No article title, Phys. Lett. B, 659, 906 (2008) · Zbl 1246.81073 · doi:10.1016/j.physletb.2007.12.016 |
| [11] | Duval, C.; Horvàthy, P. A., No article title, Phys. Lett. B, 479, 284-290 (2000) · Zbl 1050.81568 · doi:10.1016/S0370-2693(00)00341-5 |
| [12] | Ben Geloun, J.; Gangopadhyay, S.; Scholtz, F. G., No article title, Europhys. Lett., 86, 51001 (2009) · doi:10.1209/0295-5075/86/51001 |
| [13] | Arbab, A. I., No article title, Europhys. Lett., 98 (2012) · doi:10.1209/0295-5075/98/30008 |
| [14] | Mohadesi, M.; Mirza, B., No article title, Commun. Theor. Phys., 42, 664-668 (2004) · Zbl 1167.81419 |
| [15] | Gamboa, J.; Loewe, M.; Mendez, F.; Rojas, J. C., No article title, Int. J. Mod. Phys. A, 17, 2555-2566 (2002) · Zbl 1046.81056 · doi:10.1142/S0217751X02010960 |
| [16] | Girotti, H.O.: arXiv:hep-th/0301237v2 |
| [17] | Laughlin, R. B., No article title, Phys. Rev. Lett., 18, 1395 (1983) · doi:10.1103/PhysRevLett.50.1395 |
| [18] | Mohadesi, M.; Mirza, B., No article title, Commun. Theor. Phys., 42, 664-668 (2004) · Zbl 1167.81419 |
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