Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Local Space-Time Transformations Generated from the Ageing Algebra
Stoimenov S., Henkel M.
Springer Proceedings in Mathematics and Statistics 36 (2013) 369-379
DOI : 10.1007/978-4-431-54270-4_25

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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