Slowed Relaxational Dynamics Beyond the FluctuationDissipation Theorem.pdfVIP

Slowed Relaxational Dynamics Beyond the 1 Fluctuation-Dissipation Theorem 0 0 2 v P. De Gregorio a,b , F. Sciortino b , P. Tartaglia b, E. Zaccarelli a o N and K. A. Dawson a 1 a Irish Centre for Colloid Science and Biomaterials, Department of Chemistry, ] University College Dublin, Belfield, Dublin 4, Ireland n n b Dipartimento di Fisica Universit`a di Roma La Sapienza, Istituto Nazionale di - s Fisica della Materia, and INFM Center for Statistical Mechanics and Complexity i d Piazzale Aldo Moro 2, 00185 Roma, Italy . t a m - Abstract d n o To describe the slow dynamics of a system out of equilibrium, but close to a dy- c namical arrest, we generalize the ideas of previous work to the case where time- [ translational invariance is broken. We introduce a model of the dynamics that is 1 reasonably general, and show how all of the unknown parameters of this model may v 8 be related to the observables or to averages of the noise. One result is a generalisa- 1 tion of the Fluctuation Dissipation Theorem of type two (FDT2), and the method is 0 thereby freed from this constraint. Significantly, a systematic means of implement- 1 1 ing the theory to higher order is outlined. We propose the simplest possible closure 1 of these generalized equations, following the same type of approximations that have 0 been long known for the equilibrium case of Mode Coupling Theory (MCT). Natu- / t a rally, equilibrium MCT equations are found as a limit of this generalized formalism. m