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Advances in High Energy Physics
Volume 2018, Article ID 8968732, 7 pages
https://doi.org/10.1155/2018/8968732
Research Article

Quantum Gravity Effects in Statistical Mechanics with Modified Dispersion Relation

1Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
2Bose Centre for Advanced Study and Research in Natural Science, University of Dhaka, Dhaka, Bangladesh
3Physics Department, McGill University, Montreal, QC, Canada H3A 2T8

Correspondence should be addressed to Mir Mehedi Faruk; moc.liamg@6141.3azrutum

Received 25 September 2017; Revised 14 December 2017; Accepted 15 February 2018; Published 18 March 2018

Academic Editor: Elias C. Vagenas

Copyright © 2018 Shovon Biswas and Mir Mehedi Faruk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. J. Magueijo and L. Smolin, “Lorentz invariance with an invariant energy scale,” Physical Review Letters, vol. 88, Article ID 190403, 2002. View at Publisher · View at Google Scholar
  2. X. Zhang, L. Shao, and B.-Q. Ma, “Photon gas thermodynamics in doubly special relativity,” Astroparticle Physics, vol. 34, pp. 840–845, 2011. View at Publisher · View at Google Scholar
  3. S. Das and D. Roychowdhury, “Thermodynamics of a photon gas with an invariant energy scale,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 81, no. 8, 2010. View at Publisher · View at Google Scholar
  4. M. M. Faruk and M. M. Rahman, “Planck scale effects on the thermodynamics of photon gases,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 94, no. 10, 2016. View at Publisher · View at Google Scholar
  5. A. Kempf, G. Mangano, and R. B. Mann, “Hilbert space representation of the minimal length uncertainty relation,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 52, no. 2, pp. 1108–1118, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Kempf, “Non-pointlike particles in harmonic oscillators,” Journal of Physics A: Mathematical and General, vol. 30, no. 6, pp. 2093–2101, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  7. L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, “Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 65, Article ID 125027, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  8. C. Quesne and V. M. Tkachuk, “Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a {SUSYQM} framework,” Journal of Physics A: Mathematical and General, vol. 36, no. 41, pp. 10373–10389, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. C. Quesne and V. M. Tkachuk, “More on a {SUSYQM} approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum,” Journal of Physics A: Mathematical and General, vol. 37, no. 43, pp. 10095–10113, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. C. Quesne and V. M. Tkachuk, “Dirac oscillator with nonzero minimal uncertainty in position,” Journal of Physics A: Mathematical and General, vol. 38, no. 8, pp. 1747–1765, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. F. Brau, “Minimal length uncertainty relation and the hydrogen atom,” Journal of Physics A: Mathematical and General, vol. 32, no. 44, pp. 7691–7696, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. Benczik, L. N. Chang, D. Minic, and T. Takeuchi, “Hydrogen-atom spectrum under a minimal-length hypothesis,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 72, no. 1, Article ID 012104, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. M. M. Stetsko and V. M. Tkachuk, “Perturbation hydrogen-atom spectrum in deformed space with minimal length,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 74, no. 1, 2006. View at Publisher · View at Google Scholar
  14. M. M. Stetsko, Physical Review A, vol. 74, Article ID 062105, 2006. View at Publisher · View at Google Scholar
  15. F. Brau and F. Buisseret, “Minimal length uncertainty relation and gravitational quantum well,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 74, no. 3, Article ID 036002, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. K. Nouicer, “Casimir effect in the presence of minimal lengths,” Journal of Physics A: Mathematical and General, vol. 38, no. 46, pp. 10027–10035, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. U. Harbach and S. Hossenfelder, “The Casimir effect in the presence of a minimal length,” Physics Letters B, vol. 632, no. 2-3, pp. 379–383, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Hossenfelder, “Interpretation of quantum field theories with a minimal length scale,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 73, Article ID 105013, 2006. View at Publisher · View at Google Scholar
  19. M. M. Stetsko and V. M. Tkachuk, “Scattering problem in deformed space with minimal length,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 76, no. 1, pp. 693–695, 2007. View at Publisher · View at Google Scholar
  20. S. Das, S. Ghosh, and D. Roychowdhury, “Relativistic thermodynamics with an invariant energy scale,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 80, no. 12, 2009. View at Publisher · View at Google Scholar
  21. D. Mania and M. Maziashvili, “Corrections to the black body radiation due to minimum-length deformed quantum mechanics,” Physics Letters B, vol. 705, no. 5, pp. 521–528, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. B. R. Majhi and E. C. Vagenas, “Modified dispersion relation, photon's velocity, and unruh effect,” Physics Letters B, vol. 725, no. 4-5, pp. 477–480, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. G. Yadav, B. Komal, and B. R. Majhi, “Rainbow Rindler metric and Unruh effect,” International Journal of Modern Physics A, vol. 32, no. 33, 2017. View at Google Scholar · View at MathSciNet
  24. S. Doplicher, K. Fredenhagen, and J. E. Roberts, “Spacetime quantization induced by classical gravity,” Physics Letters B, vol. 331, no. 1-2, pp. 39–44, 1994. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Magueijo and L. Smolin, “Generalized Lorentz invariance with an invariant energy scale,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 67, no. 4, Article ID 044017, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  26. G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, “Tests of quantum gravity from observations of big gamma-ray bursts,” Nature, vol. 393, pp. 763–765, 1998. View at Publisher · View at Google Scholar · View at Scopus
  27. L. Barosi, F. A. Brito, and A. R. Queiroz, “Noncommutative field gas driven inflation,” Journal of Cosmology and Astroparticle Physics, 2008. View at Publisher · View at Google Scholar
  28. K. Nozari, M. A. Gorji, A. Damavandi Kamali, and B. Vakili, “Entropy bound for the photon gas in noncommutative spacetime,” Astroparticle Physics, Elsevier, vol. 82, pp. 66–71, 2016. View at Publisher · View at Google Scholar · View at Scopus
  29. A. F. Ali and M. Moussa, “Towards thermodynamics with generalized uncertainty principle,” Advances in High Energy Physics, vol. 2014, Article ID 629148, 7 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  30. A. Camacho and A. Macías, “Thermodynamics of a photon gas and deformed dispersion relations,” General Relativity and Gravitation, vol. 39, no. 8, pp. 1175–1183, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  31. G. Amelino-Camelia, International Journal of Modern Physics D, vol. 12, Article ID 1633, 2003.
  32. G. Amelino-Camelia, “Special treatment,” Nature, vol. 418, no. 6893, pp. 34-35, 2002. View at Publisher · View at Google Scholar · View at Scopus
  33. G. Amelino-Camelia, “Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale,” International Journal of Modern Physics D, vol. 11, Article ID 0012051, pp. 35–60, 2002. View at Publisher · View at Google Scholar
  34. J. Kowalski-Glikman and S. Nowak, “Non-commutative space-time of Doubly Special Relativity theories,” International Journal of Modern Physics D, vol. 12, pp. 299–316, 2003. View at Publisher · View at Google Scholar
  35. K. A. Alam and M. M. Faruk, “On Boundedness of Entropy of Photon Gas in Noncommutative Spacetime,” Advances in High Energy Physics, vol. 2017, Article ID 7289625, 2017. View at Publisher · View at Google Scholar · View at Scopus
  36. R. K. Pathria, Statistical Mechanics, Butterworth-Heinemann, Oxford, 1996.
  37. S. Das and R. K. Bhaduri, “Dark matter and dark energy from a Bose - Einstein condensate,” Classical and Quantum Gravity, vol. 32, no. 10, Article ID 105003, 2015. View at Publisher · View at Google Scholar · View at Scopus