Nonequilibrium dynamics in an amorphous solid

The nonequilibrium dynamics of an amorphous solid is studied with a soft-spin model. We show that the aging behavior in the glassy state follows a modified Kohlrausch-Williams-Watts form similar to that obtained in Lunkenheimer et al. [Phys. Rev. Lett. 95, 055702 (2005)] from analysis of the dielectric loss data. The nature of the fluctuation-dissipation theorem violation is also studied in time as well as correlation windows.

Figure 1

(Color online) The correlation $C\left(t+t_w,t_w\right)$ vs $t$ for a set of waiting times $t_w$’s in the ergodic phase, $a_2=0.82$ and $a_3=2.0$. Inset shows the exponent ${\beta }_{\alpha }^{\text{NE}}$ for final stretched exponential relaxation with respect to $t_w$. Dashed line is the corresponding equilibrium value of stretching exponent.

Figure 2

(Color online) The correlation $C\left(t+t_w,t_w\right)$ vs $t$ for a set of waiting times $t_w$’s in the nonergodic phase, $a_2=0.5$ and $a_3=6.0$. Inset shows scaling of different $C\left(t+t_w,t_w\right)$’s as a function of $h\left(t+t_w\right)/h\left(t_w\right)$, where $h\left(t\right)\equiv \text{exp}\left[t^{1-\kappa }/\left(1-\kappa \right)\right]$, with $\kappa =0.96$.

Figure 3

(Color online) Scaled function $\left({\chi }_{\omega }\left({\tilde{t}}_w\right)-{\chi }_{\omega }^{\text{eq}}\right)/\left({\chi }_{\omega }^{\text{st}}-{\chi }_{\omega }^{\text{eq}}\right)$ vs ${\tilde{t}}_w$ for frequencies $\omega ={\omega }_0{2}^{-n}$ with $m=0$ (circle), 2 (square), 4 (diamond), 6 (triangle up), 8 (triangle down), 10 (star), and 12 (cross). ${\omega }_0=0.13$ in units of ${\Gamma }_0$ (see text). Solid line is a fit to MKWW form (see text) with $\beta =0.50$. Inset show the variation in the $\tau \left({\tilde{t}}_w\right)$ with ${\tilde{t}}_w$, following the scheme of Ref. [15] (solid) and Ref. [10] (dashed).

Figure 4

(Color online) Effective temperature $T_{\text{eff}}$ (see text) vs waiting times ${\tilde{t}}_w$ for $\omega ={10}^{-5}$ (filled circle), $3\times {10}^{-4}$ (open circle), and $5\times {10}^{-4}$ (filled square) in units of. Solid line corresponds to best-fit curve of theoretical results. Experimental data of Ref. [16] shown with filled triangles. Inset shows $-F\left(t+t_w,t_w\right)$ vs $C\left(t+t_w\right),t_w$ corresponding to the data of Fig. 2. The slope in the FDT violation regime is $x=-0.465$.