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首页> 外文期刊>Journal of Physics, A. Mathematical and General: A Europhysics Journal >Stochastic motion of solitary excitations on the classical Heisenberg chain
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Stochastic motion of solitary excitations on the classical Heisenberg chain

机译：经典海森堡链上孤子激发的随机运动

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We study stochastic motion of solitary excitations on a classical, discrete, isotropic, ferromagnetic Heisenberg spin chain with nearest-neighbour exchange interactions. Gaussian white noise is coupled to the spins in a way that allows for the noise to be interpreted as a stochastic magnetic field. The noise translates into a collective stochastic force affecting a solitary excitation as a whole. The position of a solitary excitation has to be calculated from the noisy spin configuration, i.e. the position is defined as a function of the spin components. Two examples of such definitions are given, because we want to investigate the dependence of the results on the choice of definition. Using these definitions, we calculate the variance of the position as a function of time and determine the variance from simulations as well. The calculations require knowledge of the shape of the solitary wave. We approximate the shape with that of soliton solutions of the continuum Heisenberg chain, restricting our considerations to solitary waves of large width, in which case this approximation is good. The calculations yield a linear dependence of the variance on time, the slope being determined by parameters describing the shape of the soliton. The two definitions of the position we use provide different results for this slope. The origin of this difference is discussed. With both definitions very good agreement is found between the results of the simulations and the corresponding theoretical results, for not too large time scales. [References: 22]
机译：我们研究具有最近邻交换相互作用的经典，离散，各向同性，铁磁海森堡自旋链上孤子激发的随机运动。高斯白噪声与自旋耦合，其方式允许将噪声解释为随机磁场。噪声转化为集体的随机力，从整体上影响了单独的激励。单独激励的位置必须根据有噪声的自旋配置来计算，即，该位置被定义为自旋分量的函数。给出了两个这样的定义示例，因为我们想研究结果对定义选择的依赖性。使用这些定义，我们可以计算位置随时间变化的方差，并且还可以通过模拟确定方差。计算需要了解孤立波的形状。我们用连续海森堡链的孤子解的形状来近似形状，将我们的考虑限制在大宽度的孤立波上，在这种情况下，这种近似是好的。计算得出方差与时间的线性相关性，斜率由描述孤子形状的参数确定。我们使用的位置的两个定义为此斜率提供了不同的结果。讨论了这种差异的由来。通过这两种定义，可以在模拟结果和相应的理论结果之间找到很好的一致性，而且时间比例不要太大。 [参考：22]

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