In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov chain [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi equilibrium description on how glassy systems explore the phase space in the slow relaxation part of their dynamics. The second one is that it gives an alternative way to obtain dynamical equations starting from a dynamical rule that is static in spirit. This provides a way to overcome the difficulties encountered in the short time part of the dynamics where current conservation must be enforced. We study this approach in detail in a prototypical mean field disordered spin system, namely the p-spin spherical model, showing how we can obtain the well known equations that describe its dynamics. Then we apply the same approach to structural glasses. We first derive a set of dynamical Ornstein- Zernike equations which are very general in nature. Finally we consider two possible closure schemes for them, namely the hypernetted chain approximation of liquid theory and a closure of the BBGKY hierarchy that has been recently introduced by Szamel. From both approaches we finally find a set of dynamical mode-coupling-like equations that are supposed to describe the system in the long time/slow dynamics regime.

Quasi equilibrium construction for the long time limit of glassy dynamics / Franz, Silvio; Parisi, Giorgio; RICCI TERSENGHI, Federico; Urbani, Pierfrancesco. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - ELETTRONICO. - 2015:10(2015), p. P10010. [10.1088/1742-5468/2015/10/P10010]

Quasi equilibrium construction for the long time limit of glassy dynamics

PARISI, Giorgio;RICCI TERSENGHI, Federico;URBANI, PIERFRANCESCO
2015

Abstract

In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov chain [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi equilibrium description on how glassy systems explore the phase space in the slow relaxation part of their dynamics. The second one is that it gives an alternative way to obtain dynamical equations starting from a dynamical rule that is static in spirit. This provides a way to overcome the difficulties encountered in the short time part of the dynamics where current conservation must be enforced. We study this approach in detail in a prototypical mean field disordered spin system, namely the p-spin spherical model, showing how we can obtain the well known equations that describe its dynamics. Then we apply the same approach to structural glasses. We first derive a set of dynamical Ornstein- Zernike equations which are very general in nature. Finally we consider two possible closure schemes for them, namely the hypernetted chain approximation of liquid theory and a closure of the BBGKY hierarchy that has been recently introduced by Szamel. From both approaches we finally find a set of dynamical mode-coupling-like equations that are supposed to describe the system in the long time/slow dynamics regime.
2015
Slow dynamics and aging (theory); slow relaxation and glassy dynamic; spin glasses (theory); structural glasses (theory); Statistics and Probability; Statistical and Nonlinear Physics; Statistics, Probability and Uncertainty
01 Pubblicazione su rivista::01a Articolo in rivista
Quasi equilibrium construction for the long time limit of glassy dynamics / Franz, Silvio; Parisi, Giorgio; RICCI TERSENGHI, Federico; Urbani, Pierfrancesco. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - ELETTRONICO. - 2015:10(2015), p. P10010. [10.1088/1742-5468/2015/10/P10010]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/868043
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