论文标题
langevin的广义旋转动力学作为su（$ n $）相干状态
Langevin dynamics of generalized spins as SU($N$) coherent states
论文作者
论文摘要
传统上，自旋系统的经典模型仅保留偶极矩，但是量子自旋状态通常会具有额外的结构。 $ s $的旋转具有$ n = 2s+1 $级别。另外，旋转状态的完全特征是一组$ n^{2} -1 $局部物理可观察物，我们将其解释为广义旋转组件。例如，$ s = 1 $的旋转具有三个偶极组件和五个四极杆组件。这些成分在经典Landau-Lifshitz动力学的概括下演变，可以用噪声和阻尼项扩展。在本文中，我们将运动的动态方程式重新制定为Schrödinger图片中SU（$ n $）相干状态的Langevin动力学。该观点特别有用，是一种有效的数值方法的基础，用于在热平衡中采样自旋构型并模拟拓扑孤子的松弛和驱动运动。为了说明该方法，我们模拟了一个非平衡松弛过程，该过程创建了CP $^{2} $ Skyrmions，这是具有偶极子和四倍体特征的拓扑缺陷。
Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude $S$ have $N=2S+1$ levels. Alternatively, the spin state is fully characterized by a set of $N^{2}-1$ local physical observables, which we interpret as generalized spin components. For example, a spin with $S=1$ has three dipole components and five quadrupole components. These components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU($N$) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a non-equilibrium relaxation process that creates CP$^{2}$ Skyrmions, which are topological defects with both dipole and quadrupole character.
