On the effective temperature of an aging powder

– The aging dynamics and the fluctuation-dissipation relation between the spontaneous diffusion induced by a random noise and the drift motion induced by a small stirring force are numerically investigated in a 3D schematic model of compacting powder: a gravity-driven lattice-gas with purely kinetic constraints. The compaction dynamics is characterized by a super-aging behaviour and, in analogy with glasses, exhibits a purely dynamical time-scale dependent effective temperature. A simple experiment to measure this quantity is suggested. Introduction. – Slow relaxation phenomena are ubiquitous in nature. When one deals with glassy dynamics the challenge is the identification of the relevant degrees of freedom which makes a thermodynamic description still possible. In the attempt to provide a unifying framework to the behaviour of aging and non-relaxational systems a microscopic definition of effective temperature was introduced through a generalized fluctuation-dissipation relation [4]. This quantity turns out to coincide, at least in mean-field glasses, with the Edwards’ compactivity [6, 7, 8, 5], previously introduced in a granular matter context [1, 2]. For a class of finite-dimensional and zero-gravity compacting systems, recent numerical results have come to support this correspondence [9]. However, in contrast to the case of strong [10], or moderately strong [11] vibration regime, the absence of a temperature-like quantity in a gently shaken granular material is a rather problematic issue [12, 13, 14]. In this paper we investigate the nature of the aging dynamics and the effective temperature in a simple 3D gravity driven lattice-gas model of compacting powder [16]. We show that the non-equilibrium dynamics is characterized by a three-steps relaxation mechanism and ‘super-aging’ in the mean-square displacement. We then find that during the compaction the response to a random perturbation is positive and observe a violation of the fluctuation-dissipation relation similar to glasses. Such features show that it is possible to describe the compaction dynamics in terms of a purely dynamical time-scale dependent effective temperature. The model. – The model we consider was introduced in [16] as a simple generalization of the Kob-Andersen model [15]. The system consists of N particles on a body centred cubic lattice where there can be at most one particle per site. There is no cohesion energy among Typeset using EURO-LTEX 2 EUROPHYSICS LETTERS particles and the Hamiltonian is simply