Glasslike dynamical behavior in hierarchical models submitted to continuous cooling and heating processes - art. no. 041505

The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling rea l structural glasses. In particular, we focus on the study of time-dependen t temperature processes. In cooling processes, a phenomenon analogous to th e laboratory glass transition appears. The residual properties are analytic ally evaluated, and the concept of fictive temperature is discussed on a ph ysical basis. The evolution of the system in heating processes is governed by the existence of a normal solution of the evolution equations, which is approached by all the other solutions. This trend of the system is directly related to the glassy hysteresis effects shown by these systems. The exist ence of the normal solution is not restricted to the linear regime around e quilibrium, but it is defined for any arbitrary, far-from-equilibrium, situ ation.