Short time aging in binary glasses

We present some simple computer simulations that indicate that at short time aging is realized in a simple model of binary glasses. It is interesting to note that modest computer simulations are enough to evidenziate this effect. We also find indications of a dynamically growing correlation length. Aging has been discovered long time ago and it is has been experimentally studied in great details in some materials [1]. It has been later realized that it is a quite common phenomenon in physics. It has been the subject of wide theoretical investigations only recently [2, 3, 4]. In the nutshell aging predicts that the response of the system to a force that has been applied for a time t depends on t (also for very large times) when t is comparable to the waiting time tw, i.e. the time at which the systems has been carried to conditions at which the experiment has been done. Aging has being studied analytically in generalized spin glasses: in the simplest form it predicts that the correlation functions among a configuration at time tw and at time tw + t depend only on the ration t/tw in the limit of large times [3]. This form of aging is approximately found to be correct in spin glasses both in experiments and in numerical simulations [5, 6, 7], (although some small modification may be needed). Slightly different forms of aging have been proposed, e.g the scaling variable could be t/tw with μ near but not equal to 1. Here we stick to the t/tw scaling and we will refer to it by the name of simple aging. The aim of this note it to start a systematic study of aging using numerical simulations in real glasses. We will show that the aging regime starts at relatively short times and some of its properties can be investigated with a modest amount of computer time. We limit ourselves to the analysis in the initial time region, leaving to further more systematic investigations the study of the behaviour at larger times and in bigger systems. The numerical experiment we present here is rather simple: we run a numerical simulation where the system starts from a fully random configuration (i.e. at infinite temperature). The system is then carried (at time zero) at temperature T . We make a photograph of the system at time tw and we compare the later evolution of the system with this reference configuration. The main quantity on which we concentrate our attention is the two times correlation function g(r, tw, t) = ∑ i,k=N 〈δ(|xi(tw)− xk(tw + t)| − r)〉 N , (1)