Onset of nonexponential relaxation, diversity and glassinenn in complex systems: The activated dynamics scenario

APPIGNANESI G. A.; FRECHERO M. A.; MONTANI R. A

Trends in Statistical Physics

Año: 2004; p. 16 - 28

Activated dynamics underlies the relaxation of a vast amount of very diverse systems ranging from glasses to biopolymers which display common dynamical features and conform to the realm of complex systems. The macroscopic manifestation of this fact is the appearance of the ubiquitous nonexponential Kohlrausch relaxation law. This law has been found to verify in an ample range of very diverse systems including glasses, spin glasses and biopolymers, between others. To account for this rather universal behavior, a general phenomenological picture (relevant to central issues as the glass transition and the dynamics of biopolymer systems) has emerged: The landscape paradigm. Such approach reflects the influence the potential energy landscape poses on the dynamics and stems from the fact that conformation space is made up of many minima or basins (valleys) separated by large energy barriers (which in turn may be arranged hierarchically). Thus, the existence of metastable states within a broken ergodicity scenario is implied. This approach rests on a tenet introduced long ago (recently computationally corroborated but not yet properly validated from first principles): The timescale separation hypothesis. This assumption implies the fact that local events are fast enough compared to long-range non-local ones to achieve local thermal equilibrium. The large scale events can thus be treated as activated events or defects, governing the long time dynamics. The purpose of this work is to review the relevance of activated dynamics (and thus of timescale separation) as marker of diversity, complexity and glassy dynamics. Thus, we shall demonstrate that its prevalence over other kinds of mechanisms determines the emergence of complex dynamical behavior. We shall mainly focus both on an ample generic context, that of complex hierarchical systems, and on a specific one, a simple model glass-former. We shall indicate the conditions for the applicability of the landscape approach, the connections between the two contexts and the relation to a variational principle. Within the specific context we shall reveal the microscopic rationale for the occurrence of timescale separation, thus validating the scenario purported by the landscape paradigm. indicate the conditions for the applicability of the landscape approach, the connections between the two contexts and the relation to a variational principle. Within the specific context we shall reveal the microscopic rationale for the occurrence of timescale separation, thus validating the scenario purported by the landscape paradigm.