From entropic to energetic barriers in glassy dynamics: The Barrat-Mézard trap model on sparse networks

稀疏 Barrat-Mézard 陷阱模型中的多重分形与统计局域化

Multifractality and statistical localization in the sparse Barrat-Mézard trap model

本文研究稀疏 Barrat-Mézard 陷阱模型中主算子谱发散对应的弛豫模，揭示其波函数具有多重分形和统计局域化特征，并提出有效模型解释谱发散与幂律尾部。

Mode-coupling theory for the dynamic heterogeneity in an aging glass: How Do Glassy Domains Grow?

We construct the equations for the growth kinetics of an aging structural glass within mode-coupling theory through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. {\bf 97}, 195701 (2006). We solve a schematic form of the resulting equations to obtain the coarsening of the dynamic heterogeneity, characterized via the 3-point correlator $χ_3(t,t_w)$, as a function of waiting time $t_w$. For a quench into the glass, we find that $χ_3$ attains a peak value $\sim t_w^{0.5}$ at $t -t_w \sim t_w^{0.8}$, providing a theoretical basis for the numerical observations of …

Crossover from entropic to thermal dynamics in glassy models

We study the emergence of a crossover from entropically driven to thermally activated dynamics in different versions of the `entropic' phase space model introduced by Barrat and Mézard, and previously considered in the zero temperature limit. We first focus on the low temperature (T < Tg) aging phase of the original model and show that a short time singularity appears in the correlation function for Tg/2 < T < Tg, leading to dynamical ultrametricity at T=Tg. We then consider the finite size version of this model, showing that the long time dynamics is always thermally activated beyond a size d…

Trap models with slowly decorrelating observables

We study the correlation and response dynamics of trap models of glassy dynamics, considering observables that only partially decorrelate with every jump. This is inspired by recent work on a microscopic realization of such models, which found strikingly simple linear out-of-equilibrium fluctuation-dissipation relations in the limit of slow decorrelation. For the Barrat-Mezard model with its entropic barriers we obtain exact results at zero temperature $T$ for arbitrary decorrelation factor $κ$. These are then extended to nonzero $T$, where the qualitative scaling behaviour and all scaling exp…

Fluctuation-dissipation relations in trap models

Trap models are intuitively appealing and often solvable models of glassy dynamics. In particular, they have been used to study aging and the resulting out-of-equilibrium fluctuation-dissipation relations between correlations and response functions. In this note I show briefly that one such relation, first given by Bouchaud and Dean, is valid for a general class of mean-field trap models: it relies only on the way a perturbation affects the transition rates, but is independent of the distribution of trap depths and the form of the unperturbed transition rates, and holds for all observables tha…