论文标题
从玻璃动力学中的熵到充满活力的障碍：稀疏网络上的Barrat-Mézard陷阱模型
From entropic to energetic barriers in glassy dynamics: The Barrat-Mézard trap model on sparse networks
论文作者
论文摘要
陷阱模型将玻璃动力学描述为代表局部能量最小值的配置网络上的随机过程。我们在此类中研究范式的Barrat-Mézard模型，该模型具有Glauber过渡速率。我们的重点是网络连接的效果，我们超越了通常的平均字段（完全连接）近似值，并考虑稀疏的网络，特别是随机的常规图。我们使用腔体方法获得了主操作员放松率的光谱密度，从而揭示了非常丰富的行为，这是网络连接性$ c $和温度$ t $的函数。我们将其追溯到最初的熵障碍物的跨界，这是由于下坡方向的稀少而导致的，到控制了长期以来逃离当地极小的能源屏障。获得的见解用于合理化高$ t $淬灭之后的能量放松，以及相应的相关性和持久性功能。
Trap models describe glassy dynamics as a stochastic process on a network of configurations representing local energy minima. We study within this class the paradigmatic Barrat-Mézard model, which has Glauber transition rates. Our focus is on the effects of the network connectivity, where we go beyond the usual mean field (fully connected) approximation and consider sparse networks, specifically random regular graphs. We obtain the spectral density of relaxation rates of the master operator using the cavity method, revealing very rich behaviour as a function of network connectivity $c$ and temperature $T$. We trace this back to a crossover from initially entropic barriers, resulting from a paucity of downhill directions, to energy barriers that govern the escape from local minima at long times. The insights gained are used to rationalize the relaxation of the energy after a quench from high $T$, as well as the corresponding correlation and persistence functions.
