Krajnik Žiga, Ilievski Enej, Prosen Tomaž
Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia.
Phys Rev Lett. 2022 Mar 4;128(9):090604. doi: 10.1103/PhysRevLett.128.090604.
We investigate dynamical fluctuations of transferred magnetization in the one-dimensional lattice Landau-Lifshitz magnet with uniaxial anisotropy, representing an emblematic model of interacting spins. We demonstrate that the structure of fluctuations in thermal equilibrium depends radically on the characteristic dynamical scale. In the ballistic regime, typical fluctuations are found to follow a normal distribution and scaled cumulants are finite. In stark contrast, on the diffusive and superdiffusive timescales, relevant, respectively, for the easy-axis and isotropic magnet at vanishing total magnetization, typical fluctuations are no longer Gaussian and, remarkably, scaled cumulants are divergent. The observed anomalous features disappear upon breaking integrability, suggesting that the absence of normal fluctuations is intimately tied to the presence of soliton modes. In a nonequilibrium setting of the isotropic magnet with weakly polarized step-profile initial state we find a slow drift of dynamical exponent from the superdiffusive towards the diffusive value.
我们研究了具有单轴各向异性的一维晶格朗道-里夫希茨磁体中转移磁化强度的动力学涨落，该磁体是相互作用自旋的一个典型模型。我们证明，热平衡中的涨落结构从根本上取决于特征动力学尺度。在弹道 regime 中，发现典型涨落遵循正态分布且标度累积量是有限的。形成鲜明对比的是，在扩散和超扩散时间尺度上，分别对应于总磁化强度为零时的易轴磁体和各向同性磁体，典型涨落不再是高斯分布，而且显著的是，标度累积量是发散的。在打破可积性时，观察到的反常特征消失了，这表明不存在正态涨落与孤子模式的存在密切相关。在具有弱极化阶跃分布初始态的各向同性磁体的非平衡设定中，我们发现动力学指数从超扩散值向扩散值缓慢漂移。
