论文标题
平均场玻璃模型中的动力学静态和激活过程
Dynamical Instantons and Activated Processes in Mean-Field Glass Models
论文作者
论文摘要
我们专注于简单的玻璃均值模型的能量景观，并通过将高维高斯景观的KAC-RICE方法与动态场理论相结合，从而分析了激活的屏障横断。特别是，我们考虑了纯球形$ p $ spin模型的能量景观中低温的兰格文动力学。我们选择动力学的初始条件是参考局部最小值附近的许多不稳定索引-1马鞍之一。我们表明，相关的动态均值场方程允许两种解决方案：一种对应于原始参考最小值，而另一个则是达到屏障的新最小值。通过改变鞍座，我们扫描并表征了通过激活的屏障交叉到达这种最小值的性质。最后，使用时间逆转转换，我们构造了相应激活过程的两点函数动力学动态插入。
We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.
