Long time limit of equilibrium glassy dynamics and replica calculation

Abstract

It is shown that the limit $t-t^{\prime }\to \infty$ of the equilibrium dynamic self-energy can be computed from the $n\to 1$ limit of the static self-energy of a $n$-times replicated system with one step replica symmetry breaking structure. It is also shown that the Dyson equation of the replicated system leads in the $n\to 1$ limit to the bifurcation equation for the glass ergodicity breaking parameter computed from dynamics. The equivalence of the replica formalism to the long time limit of the equilibrium relaxation dynamics is proved to all orders in perturbation for a scalar theory.

25 pages, 12 Figures, RevTeX. Corrected misprints. Published version

References in corpus (6)

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• Amorphous packings of hard spheres in large space dimension
• Mode-coupling theory and the fluctuation-dissipation theorem for nonlinear Langevin equations with multiplicative noise
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• Brownian dynamics: from glassy to trivial
• A simple spin model for three steps relaxation and secondary proccesses in glass formers
• Kinetic Equations Governing Smoluchowski Dynamics in Equilibrium
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• Glassy behavior of two-dimensional stripe-forming systems
• A numerical study of longtime dynamics and ergodic-nonergodic transitions in dense simple fluids
• Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume Emery Griffiths disordered model
• Logarithmic critical slowing down in complex systems: from statics to dynamics