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Non-Local Space-Time Transformations Generated from the Ageing Algebra

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Lie Theory and Its Applications in Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 36))

Abstract

The ageing algebra is a local dynamical symmetry of many ageing systems, far from equilibrium, and with a dynamical exponent z = 2. Here, new representations for an integer dynamical exponent z = n are constructed, which act non-locally on the physical scaling operators. The new mathematical mechanism which makes the infinitesimal generators of the ageing algebra dynamical symmetries, is explicitly discussed for a n-dependent family of linear equations of motion for the order-parameter. Finite transformations are derived through the exponentiation of the infinitesimal generators and it is proposed to interpret them in terms of the transformation of distributions of spatio-temporal coordinates. The two-point functions which transform co-variantly under the new representations are computed, which quite distinct forms for n even and n odd. Depending on the sign of the dimensionful mass parameter, the two-point scaling functions either decay monotonously or in an oscillatory way towards zero.

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Notes

  1. 1.

    This paper contains the main results from the original one [30] which the first author presented on LT-9 conference

  2. 2.

    All entries in Tables 1 and 2 can be checked by direct substitution.

  3. 3.

    For example, the scaling function ℱ 2(y) in (24) reproduces the exactly known two-time response in the 3D Mullins–Herring model of surface growth with a conserved order-parameter [29].

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Acknowledgements

Most of the work on this paper was done during the visits of S.S. at the Université Henri Poincaré Nancy I. S.S. is supported in part by the Bulgarian NSF grant DO 02-257.

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Authors and Affiliations

  1. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, BG–1784, Sofia, Bulgaria

    Stoimen Stoimenov

  2. Groupe de Physique Statistique, Département de Physique de la Matière et des Matériaux, Institut Jean Lamour, Nancy Université, 70239, F–54506, Vandœuvre lès Nancy Cedex, France

    Malte Henkel

Authors
  1. Stoimen Stoimenov
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  2. Malte Henkel
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Correspondence to Stoimen Stoimenov .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, Sofia, 1784, Sofiya, Bulgaria

    Vladimir Dobrev

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Stoimenov, S., Henkel, M. (2013). Non-Local Space-Time Transformations Generated from the Ageing Algebra. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_25

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