Distributions of inherent structure energies during aging

We perform extensive simulations of a binary mixture Lennard-Jones system subjected to a temperature jump in order to study the time evolution of fluctuations during aging. Analyzing data from 1500 different aging realizations, we calculate distributions of inherent structure energies for different aging times and contrast them with equilibrium. We find that the distributions initially become narrower and then widen as the system equilibrates. For deep quenches, fluctuations in the glassy system differ significantly from those observed in equilibrium. Simulation results are partially captured by theoretical predictions only when the final temperature is higher than the mode coupling temperature.

Figure 1

Distributions of $e_{\mathrm{IS}}$ during aging. Histograms (of unit area) showing $P(e_{\mathrm{IS}},t_{\mathrm{w}})$ (filled diamonds) for an ensemble of aging systems with $T_{\mathrm{i}}=0.8$ and $T_{\mathrm{b}}=0.446$ with $t_{\mathrm{w}}=542$, 3405, 7482, 21372, 46954, 174338, and 841500 from right to left. Also shown are equilibrium distributions $P(e_{\mathrm{IS}},T)$ (open circles) for $T=0.8$, 0.55, and 0.446 from right to left.

Figure 2

Time evolution of the average $e_{\mathrm{ag}}$ (a) and of the standard deviation ${\sigma }_{\mathrm{ag}}$ (b) of the inherent structure energy distribution $P(e_{\mathrm{IS}},t_{\mathrm{w}})$. Legend indicates the corresponding $T_{\mathrm{i}}$ and $T_{\mathrm{b}}$ values.

Figure 3

Relationship between ${\sigma }_{\mathrm{ag}}$ and $e_{\mathrm{ag}}$ during aging. The legend indicates $T_{\mathrm{i}}$ and $T_{\mathrm{b}}$. Panel (a) shows the theoretical predictions based on the GHA, using the landscape parameters calculated fitting equilibrium data [21]. Panel (b) shows MD data. Filled circles indicate equilibrium values.

Figure 4

Vibrational properties of basins as a function of $e_{\mathrm{IS}}$. Panel (a) shows ${⟨M⟩}_{\mathrm{eq}}\left(e_{\mathrm{IS}}\right)$ (filled circles, bars indicating standard deviations) and aging ensemble averages ${⟨M⟩}_{\mathrm{ag}}\left(e_{\mathrm{IS}}\right)$. For the dot-dash line we use a binning procedure to determine $M\left(e_{\mathrm{IS}}\right)$ from all basins regardless of $t_{\mathrm{w}}$ during aging for the $(0.8\to 0.25)$ run. Panel (b) shows the equilibrium $P\left(M\right)$ for $T=0.55$ (solid line), and for the case where all basins with energy ${\overline{e}}_{\mathrm{IS}}(T=0.55)\pm 0.002$ are used (short dash); and for the aging runs $(0.8\to 0.446)$ (long dash) and $(0.8\to 0.25)$ (dot dash), also binning the energy.