标题： $SU(\infty)$退化动力学在$SU(n_f)$对称自旋模型中的普遍性 显示英文标题

标题： Universality of $SU(\infty)$ relaxation dynamics for $SU(n_f)$-symmetric spin-models

摘要： 自旋模型中，$N$自旋通过保持$SU(n_f)$对称性的哈密顿量两两相互作用，在大$n_f$、$N$极限下著名地简化，这是 Sachdev 和 Ye 在探索自旋玻璃的平均场行为时推导出的。 我们提供了数值证据，表明对于一大类模型，大$n_f$极限并非必需：对于一组受相互作用密集中微子气体平均场处理启发的经典模型，在高温下的弛豫过程可以用相同的动力学方程来描述，直到关联函数微扰级数的收敛半径所设定的时间。 经过简单的时间缩放后，动力学表现出令人惊讶的普适性，只要耦合矩阵的秩较小，对于任何$n_f$值都相同。 作为我们结果的一个推论，我们发现源自流体湍流中随机流研究的直接相互作用近似应被视为一般随机耦合系统的短时间近似。 显示英文摘要

摘要： Spin-models, where the $N$ spins interact pairwise with a $SU(n_f)$ symmetry preserving hamiltonian, famously simplify in the large $n_f$, $N$ limits, as derived by Sachdev and Ye when exploring mean-field behavior of spin-glasses. We present numerical evidence that for a large class of models, the large $n_f$ limit is not necessary: the same dynamical equations can describe the relaxation processes at high temperatures for a set of classical models inspired from mean-field treatments of interacting dense neutrino gases, up to times set by the radius of convergence of the perturbation series for the correlation function. After a simple rescaling of time, the dynamics display a surprising universality, being identical for any value of $n_f$ as long as the rank of the coupling matrix is small. As a corollary of our results, we find that the direct interaction approximation originating from the study of stochastic flows in fluid turbulence should be thought of as only a short-time approximation for generic random coupling systems.