Advertisement

Thermodynamics in the NC disc

  • S. A. Franchino-ViñasEmail author
  • P. Pisani
Regular Article

Abstract.

We study the thermodynamics of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. We explicitly obtain expressions for thermodynamic potentials of gases of particles obeying different statistics. In order to do that, we derive an asymptotic expansion for the density of the zeros of Laguerre polynomials. As a result we prove that the Bose-Einstein condensation in the noncommutative disc does not take place.

References

  1. 1.
    A. Connes, J. Lott, Nucl. Phys. B Proc. Suppl. 18, 29 (1991)CrossRefGoogle Scholar
  2. 2.
    J. Madore, Class. Quantum Grav. 9, 69 (1992)CrossRefGoogle Scholar
  3. 3.
    S. Doplicher, K. Fredenhagen, J.E. Roberts, Phys. Lett. B 331, 39 (1994)MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Connes, M.R. Douglas, A.S. Schwarz, JHEP 02, 003 (1998)CrossRefGoogle Scholar
  5. 5.
    N. Seiberg, E. Witten, JHEP 09, 032 (1999) arXiv:hep-th/9908142CrossRefGoogle Scholar
  6. 6.
    H.S. Snyder, Phys. Rev. 71, 38 (1947)CrossRefGoogle Scholar
  7. 7.
    M.R. Douglas, N.A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001)CrossRefGoogle Scholar
  8. 8.
    R.J. Szabo, Phys. Rep. 378, 207 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    L. Perivolaropoulos, Phys. Rev. D 95, 103523 (2017) arXiv:1704.05681 [gr-qc]MathSciNetCrossRefGoogle Scholar
  10. 10.
    G. Amelino-Camelia, Living Rev. Relativ. 16, 5 (2013) arXiv:0806.0339 [gr-qc]CrossRefGoogle Scholar
  11. 11.
    H. Falomir, S.A. Franchino Viñas, P.A.G. Pisani, F. Vega, JHEP 12, 024 (2013) arXiv:1307.4464 [hep-th]CrossRefGoogle Scholar
  12. 12.
    F. Lizzi, P. Vitale, A. Zampini, JHEP 08, 057 (2003)CrossRefGoogle Scholar
  13. 13.
    F. Lizzi, P. Vitale, A. Zampini, JHEP 09, 080 (2005)CrossRefGoogle Scholar
  14. 14.
    F. Lizzi, P. Vitale, A. Zampini, J. Phys. Conf. Ser. 53, 830 (2006)CrossRefGoogle Scholar
  15. 15.
    A.P. Balachandran, K.S. Gupta, S. Kurkcuoglu, JHEP 09, 007 (2003)CrossRefGoogle Scholar
  16. 16.
    F. Lizzi, B. Spisso, Int. J. Mod. Phys. A 27, 1250137 (2012)CrossRefGoogle Scholar
  17. 17.
    N.C. Dias, J.N. Prata, J. Math. Phys. 43, 4602 (2002)MathSciNetCrossRefGoogle Scholar
  18. 18.
    S. Kryukov, M.A. Walton, Ann. Phys. 317, 474 (2005)CrossRefGoogle Scholar
  19. 19.
    R. Houça, A. Jellal, arXiv:1803.03566 [cond-mat.stat-mech]Google Scholar
  20. 20.
    S.F. Viñas, F. Vega, Magnetic properties of a Fermi gas in a noncommutative phase space, arXiv:1606.03487 [hep-th]Google Scholar
  21. 21.
    A. Halder, S. Gangopadhyay, Int. J. Theor. Phys. 56, 1831 (2017) arXiv:1609.06580 [hep-th]CrossRefGoogle Scholar
  22. 22.
    F.A. Brito, E.E.M. Lima, Int. J. Mod. Phys. A 31, 1650057 (2016) arXiv:1509.01222 [hep-th]CrossRefGoogle Scholar
  23. 23.
    F.G. Scholtz, J. Govaerts, J. Phys. A 41, 505003 (2008) arXiv:0810.3064 [hep-th]MathSciNetCrossRefGoogle Scholar
  24. 24.
    J.N. Kriel, F.G. Scholtz, J. Phys. A 45, 095301 (2012) arXiv:1112.1579 [math-ph]MathSciNetCrossRefGoogle Scholar
  25. 25.
    F.G. Scholtz, J.N. Kriel, H.W. Groenewald, Phys. Rev. D 92, 125013 (2015) arXiv:1508.05799 [hep-th]MathSciNetCrossRefGoogle Scholar
  26. 26.
    H.J. Groenewold, Physica 12, 405 (1946)MathSciNetCrossRefGoogle Scholar
  27. 27.
    J.E. Moyal, Proc. Camb. Philos. Soc. 45, 99 (1949)CrossRefGoogle Scholar
  28. 28.
    W. Gawronski, Analysis 13, 29 (1993)MathSciNetCrossRefGoogle Scholar
  29. 29.
    R.K. Pathria, Statistical Mechanics, 2nd edition (Butterworth-Heinemann, 1996)Google Scholar
  30. 30.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products, 7th edition (Academic Press, 2007)Google Scholar
  31. 31.
    S. Ahmed, F. Calogero, Lett. Nuovo Cimento 21, 531 (1978)CrossRefGoogle Scholar
  32. 32.
    M. Abramowitz, I.A. Stegun (Editors), Handbook of Mathematical Functions, 9th edition (Dover Publications, 1972)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Theoretisch-Physikalisches InstitutFriedrich Schiller Universität JenaJenaGermany
  2. 2.Departamento de Física, Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataArgentina
  3. 3.IFLP-CONICET/ Departamento de Física, Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataArgentina

Personalised recommendations