Potential energy landscape picture of zero-temperature avalanche criticality governing dynamics in supercooled liquids

Abstract

Supercooled liquids are metastable states realized by suppressing crystallization below the melting temperature. While it is well established that their dynamics slow down dramatically and become spatially heterogeneous upon cooling, the microscopic origin of these nontrivial glassy phenomena remains a matter of active debate. In the present study, by means of molecular dynamics simulations, we first demonstrate that nontrivial slow dynamics, such as structural relaxation and dynamical heterogeneity, can be consistently described within a zero-temperature avalanche criticality picture. Since this finding suggests that the potential energy landscape plays a crucial role in determining the dynamics, we further quantify the potential energy landscape from three distinct perspectives. Based on these analyses, we propose a potential-energy-landscape picture of avalanche criticality that is consistent with various previous studies. Our proposed picture explains in a unified manner previously unexplained observations near the mode-coupling transition, such as the saturation of the dynamical susceptibility and the localization of unstable modes in saddle configurations.

Figures (19)

• Figure 1: Semi-log plots of the overlap function $Q(t)$ and the dynamical susceptibility $\chi_4(t)$ as functions of time. Panels (a-c) in the top row show the results for $Q(t)$, with symbols representing the simulation data and lines corresponding to fits using the two-mode model given in Eq. \ref{['eq:2mode']}. Panels (d-f) in the bottom row show the results for $\chi_4(t)$, with symbols representing the simulation data and lines corresponding to cubic-spline interpolations. Although small peaks sometimes appear at long times in the interpolated lines, they are artifacts of the interpolation and do not affect the extraction of the main peak. From left to right, the results correspond to $T = 0.6 (\approx T_{\rm ava}), 0.5, 0.44 (\approx T_{\rm MCT})$. In all panels, different symbols represent different system sizes, as indicated in the legend of panel (a).
• Figure 2: (a) Semi-log plot of the peak time, $\tau_4$, of the dynamical susceptibility $\chi_4(t)$ as a function of inverse temperature. For clarity, only the results for $N=200$, $500$, and $1500$ are shown. (b) Log-log plot of the peak value of the dynamical susceptibility, $\chi_4^\ast$, as a function of temperature. (c) Finite-size scaling of $\chi_4^\ast$ using the critical exponents obtained in the main text, $\nu \approx 3.2$ and $\gamma \approx 6.0$. Only the results for $T \le T_{\rm ava}=0.6$ are shown. In panels (a) and (b), the vertical dotted lines indicate the positions of the temperatures $T_{\rm ava} \approx 0.6$ and $T_{\rm MCT} \approx 0.435$. In panels (b) and (c), the dashed lines represent the power-law behavior $\chi_4^\ast \sim T^{-\gamma}$. In all panels, different symbols represent different system sizes, as indicated in the legends below the panels.
• Figure 3: Slow-mode parameters obtained from fitting $Q(t)$ using the two-mode model, Eq. \ref{['eq:2mode']}. (a) Semi-log plot of the $\alpha$-relaxation time $\tau_\alpha$ as a function of inverse temperature. (b) Linear plot of the stretching exponent $\beta_{\rm KWW}$ as a function of inverse temperature. In both panels, the vertical dashed lines indicate the locations of $T_{\rm ava}\approx 0.6$ and $T_{\rm MCT}\approx 0.435$, and different symbols represent different system sizes as indicated in the legend below the panels.
• Figure 4: Linear plot of the number of unstable modes at saddle-point configurations, $N_{\rm saddle}^\dagger$, as a function of temperature. Symbols indicate the mean values, error bars represent the standard deviations, and the shaded regions depict the range between the minimum and maximum values. Vertical dashed lines indicate the locations of $T_{\rm ava}\approx 0.6$ and $T_{\rm MCT}\approx 0.435$. Results are shown for (a) $N=200$, (b) $N=500$, and (c) $N=1000$.
• Figure 5: Schematic illustration of the potential energy landscape. The vertical axis represents the potential energy, while the horizontal axis denotes particle configurations. The white circle indicates an instantaneous state of the system. (a) The inherent structure corresponding to the system state, (b) a saddle point (the nearest stationary point), and (c) the energy level of the inherent structure. For simplicity, the PEL is shown as a one-dimensional function; in reality, it is defined on a high-dimensional hypersurface of dimension $dN-d$.