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On Non-local Representations of the Ageing Algebra in d ≥ 1 Dimensions

  • Stoimen Stoimenov
  • Malte Henkel
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 111)

Abstract

Non-local representations of the ageing algebra for generic dynamical exponents z and for any space dimension d ≥ 1 are constructed. The mechanism for the closure of the Lie algebra is explained. The Lie algebra generators contain higher-order differential operators or the Riesz fractional derivative. Covariant two-time response functions are derived. An application to phase-separation in the conserved spherical model is described.

Keywords

Spherical Model Dynamical Symmetry Conformal Algebra Dynamical Exponent Dynamical Scaling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Ce travail a reçu du support financier par PHC Rila et par le Collège Doctoral franco-allemand Nancy-Leipzig-Coventry (Systèmes complexes à l’équilibre et hors équilibre) de l’UFA-DFH.

References

  1. 1.
    Bargmann, V.: Ann. Math. 59, 1–46 (1954)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Baumann, F., Stoimenov, S., Henkel, M.: J. Phys. A39, 4095 (2006). [cond-mat/0510778] Google Scholar
  3. 3.
    Baumann, F., Henkel, M.: J. Stat. Mech. P01012 (2007). [cond-mat/0611652] Google Scholar
  4. 4.
    Berlin, T.H., Kac, M.: Phys. Rev. 86, 821 (1952); Lewis, H.W., Wannier, G.H.: Phys. Rev. 88, 682 (1952); 90, 1131 (1953)Google Scholar
  5. 5.
    Bray, A.J.: Adv. Phys. 43, 357 (1994)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Cugliandolo, L.F.: In: Barrat, J.-L. et al. (eds.) Slow Relaxation and Non Equilibrium Dynamics in Condensed Matter. Les Houches, vol. 77. Springer, Heidelberg (2003). ([cond-mat/0210312])Google Scholar
  7. 7.
    Dobrev, V.K.: Non-relativistic holography (a group-theoretical perspective). Invited review. Int. J. Mod. Phys. A29(3&4), 1430001 (2014). [arXiv:1312.0219] Google Scholar
  8. 8.
    Durang, X., Henkel, M.: J. Phys. A42, 395004 (2009). [arxiv:0905.4876] Google Scholar
  9. 9.
    Duval, C., Horváthy, P.A.: J. Phys. A42, 465206 (2009). [arxiv:0904.0531] Google Scholar
  10. 10.
    Godrèche, C., Krzakala, F., Ricci-Tersenghi, F.: J. Stat. Mech. P04007 (2004). [cond-mat/0401334] Google Scholar
  11. 11.
    Havas, P., Plebanski, J.: J. Math. Phys. 19, 482 (1978)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Henkel, M.: Phys. Rev. Lett. 78, 1940 (1997). [cond-mat/9610174] Google Scholar
  13. 13.
    Henkel, M.: Nucl. Phys. B641, 405 (2002). [hep-th/0205256] Google Scholar
  14. 14.
    Henkel, M., Baumann, F.: J. Stat. Mech. P07015 (2007). [cond-mat/0703226] Google Scholar
  15. 15.
    Henkel, M., Enss, T., Pleimling, M.: J. Phys. A39, L589 (2006). [cond-mat/0605211] Google Scholar
  16. 16.
    Henkel, M., Pleimling, M.: Non-equilibrium Phase Transitions. Ageing and Dynamical Scaling Far from Equilibrium, vol. 2. Springer, Heidelberg (2010)Google Scholar
  17. 17.
    Henkel, M., Stoimenov, S.: Nucl. Phys B847, 612 (2011). [arxiv:1011.6315] Google Scholar
  18. 18.
    Henkel, M., Stoimenov, S.: J. Phys. A46, 245004 (2013). [arxiv:1212.6156] Google Scholar
  19. 19.
    Hohenberg, P., Halperin, B.I.: Rev. Mod. Phys. 49, 435 (1977)CrossRefGoogle Scholar
  20. 20.
    Janssen, H.-K.: In: Györgi, G. et al. (eds.) From Phase-Transitions to Chaos. World Scientific, Singapore (1992)Google Scholar
  21. 21.
    Joyce, G.S.: In: Domb, C., Green, M. (eds.) Phase Transitions and Critical Phenomena, vol. 2, p. 375. Academic Press, London (1972)Google Scholar
  22. 22.
    Kissner, J.G.: Phys. Rev. B46, 2676 (1992)CrossRefGoogle Scholar
  23. 23.
    Lukierski, J., Stichel, P.C., Zakrewski, W.J.: Phys. Lett. A357, 1 (2006). [hep-th/0511259]; Phys. Lett. B650, 203 (2007). [hep-th/0702179] Google Scholar
  24. 24.
    Majumdar, S.N., Huse, D.A.: Phys. Rev. E52, 270 (1995)Google Scholar
  25. 25.
    Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)MATHGoogle Scholar
  26. 26.
    Minic, D., Vaman, D., Wu, C.: Phys. Rev. Lett. 109, 131601 (2012). [arxiv:1207.0243] Google Scholar
  27. 27.
    Mullins, W.W.: In: Gjostein, N.A., Robertson, W.D. (eds.) Metal Surfaces: Structure, Energetics, Kinetics. American Society of Metals, Metals Park (1963)Google Scholar
  28. 28.
    Negro, J., del Olmo, M.A., Rodríguez-Marco, A.: J. Math. Phys. 38, 3786, 3810 (1997)Google Scholar
  29. 29.
    Picone, A., Henkel, M.: Nucl. Phys. B688, 217 (2004). [cond-mat/0402196] Google Scholar
  30. 30.
    Röthlein, A., Baumann, F., Pleimling, M.: Phys. Rev. E74, 061604 (2006); Erratum E76, 019901 (2007). [cond-mat/0609707] Google Scholar
  31. 31.
    Sire, C.: Phys. Rev. Lett. 93, 130602 (2004). [cond-mat/0406333] Google Scholar
  32. 32.
    Struik, L.C.E.: Physical Ageing in Amorphous Polymers and Other Materials. Elsevier, Amsterdam (1978)Google Scholar
  33. 33.
    Sun, T., Guo, H., Grant, M.: Phys. Rev. A40, 6763 (1989)CrossRefGoogle Scholar
  34. 34.
    Täuber, U.C., Howard, M., Vollmayr-Lee, B.P.: J. Phys. A38, R79 (2005). [cond-mat/0501678] Google Scholar
  35. 35.
    Wolf, D.E., Villain, J.: Europhys. Lett. 13, 389 (1990)CrossRefGoogle Scholar
  36. 36.
    Wright, E.M., J. Lond. Math. Soc. 10, 287 (1935); Proc. Lond. Math. Soc. 46, 389 (1940); Erratum J. Lond. Math. Soc. 27, 256 (1952)Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Nuclear Research and Nuclear EnergyBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Groupe de Physique Statistique, Institut Jean Lamour (UMR 7198 CNRS)Université de Lorraine NancyVandœuvre-lès-Nancy CedexFrance

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