论文标题
受到约束$ p = 2 $软旋转的低温动力学
Low temperature dynamics for confined $p=2$ soft spin in the quenched regime
论文作者
论文摘要
本文旨在解决$ p = 2 $旋转动力学的低温动态问题，具有限制潜力，尤其是针对四分之一的案例。动力学由langevin方程来描述，用于$ n $的真实矢量$ q_i $ q_i $ q_i $ q_i $ q_i $ q_i $ q_i $ q_i $ q_i $ q_i $ q_i $ q_i $ n $ a $由wigner矩阵实现，我们特别研究了自我一致的演化方程，以实现有效的潜在，从平方长度平均$ a（t）\ equiv \ equiv \ equiv \ sum_i q_i q_i q_i q_i q_i q_i q_i q_i^2（t）/n $大$ n $。假设系统达到了一定的平衡点，我们首先关注静态情况，然后我们研究系统动态到达该点的方式。这允许识别临界温度，在高于该温度之上，朝着平衡的放松遵循指数定律，但在其下面具有无限的时间寿命，与功率定律衰减相对应。
This paper aims to address the low-temperature dynamics issue for the $p=2$ spin dynamics with confining potential, focusing especially on quartic and sextic cases. The dynamics are described by a Langevin equation for a real vector $q_i$ of size $N$, where disorder is materialized by a Wigner matrix and we especially investigate the self consistent evolution equation for effective potential arising from self averaging of the square length $a(t)\equiv \sum_i q_i^2(t)/N$ for large $N$. We first focus on the static case, assuming the system reached some equilibrium point, and we then investigate the way the system reach this point dynamically. This allows to identify a critical temperature, above which the relaxation toward equilibrium follows an exponential law but below which it has infinite time life and corresponds to a power law decay.
