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On a dynamical model of glasses

W hen T < To, on the other hand, no normalisable Peą( t ) can be found, which corresponds to the weak ergodicity breaking situation described in [10,13,14]. In this situation, P ( e , t ) never reaches a stationary lim it, but continuously drifts towards larger and larger energies. Tim e translational invariance is spontaneously broken as C ( t , t ' ) never becomes a function of t — t' alone, a situation now referred to as ‘aging’. In fact, one can show [18] that C (tw ~b t , t w ) = C(£/£w), with 1 - C(u) oc u T° for її —► 0 and C oc u To for u —> oo, precisely as in the ‘trap’ model studied in [13]. This suggests that the difference between the ‘quenched’ model considered in [13] (corresponding to D ξ 0 in Eq. (1)) and the ‘annealed’ model considered here is, to some extent, irrelevant.