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Analyse des symétries d'espace-temps dans les systèmes vieillissants

Abstract : The slow dynamics observed in ferromagnetic systems rapidly quenched from a disordered initial state into its low-temperature ordered phase is characterized by the breaking of time-translation invariance and by dynamical scaling. Since the dynamical exponent generically has the value z=2 in this situation, the natural candidates for extended dynamical scale-transformation are the elements of the Schrödinger group Sch(d). A reformulation in terms of stochastic field-theory shows that the symmetries of the system, described by a stochastic Langevin equation, can be obtained from the consideration of the deterministic part of that equation, which is a non-linear partial differential equation. It follows that the form of the response functions can be derived from the hypothesis of their covariant transformation under local scale-transformations. The explicit construction of non-linear diffusion equations which are invariant under the Lie algebra schd of the Schrödinger group or else is subalgebra aged which is obtained when time-translations are excluded, requires the introduction of a new dimensionful variable, related to a physical coupling constant g. Constructing new representations of the sch1 and age1 containing g, new non-linear equations with real-valued solutions are obtained, which are Schrödinger- and not only Galilei-invariant. The resulting expression for the response function is derived. Applications to Bose-Einstein condensation and the slow kinetics of strongly interacting particle systems are discussed. A different route uses the embedding of sch1 as an (almost) parabolic subalgebra of the conformal algebra (conf3)C by considering the mass not as a constant, but as an additional variable. Invariant equations are classified and are compared to the coarse-grained equations for the time-dependent order-parameter in phase-ordering kinetics. Finally alt1, an other parabolic subalgebra, is studied as abstract Lie algebra. Its representation are discussed, as well as Appel system realization on coherent states.
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Submitted on : Thursday, March 29, 2018 - 10:41:00 AM
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  • HAL Id : tel-01746598, version 1



Stoimen Stoimenov. Analyse des symétries d'espace-temps dans les systèmes vieillissants. Autre [cond-mat.other]. Université Henri Poincaré - Nancy 1, 2006. Français. ⟨NNT : 2006NAN10106⟩. ⟨tel-01746598⟩



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