Dynamics of the classical Heisenberg spin chain

Dynamics of the classical Heisenberg spin chain
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经典海森堡自旋链的动力学

DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
C. Tompson
C. Tompson
中科院分区：
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文献类型：
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作者：
J. Roberts;C. Tompson

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本文研究了经典离散各向异性海森堡自旋链的演化方程。在连续极限下，这些方程变得完全可积，并且与众所周知的方程如正弦-戈登方程和非线性薛定谔方程有关。给出了离散方程的一些特解，包括自旋波、空间齐次解和平面态，它们提供了一个完全可积映射的例子。线性稳定性分析，一些数值研究和特定的时间依赖的解决方案表明，对于某些区域的相空间和参数值，系统具有混沌解决方案。
In this paper the authors study the evolution equations for the classical discrete anisotropic Heisenberg spin chain. In the continuum limit these equations become completely integrable and are related to well known equations such as the sine-Gordon and non-linear Schrodinger equations. Some particular solutions of the discrete equations are presented, including spin waves, spatially homogeneous solutions and planar states which provide an example of a completely integrable mapping. A linear stability analysis, some numerical studies and particular time-dependent solutions suggest that, for certain regions of phase space and parameter values, the system possesses chaotic solutions.