Surface‐embeddability approach to the dynamics of the inhomogeneous Heisenberg spin chain
Surface‐embeddability approach to the dynamics of the inhomogeneous Heisenberg spin chain
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非齐次海森堡自旋链动力学的表面嵌入方法
DOI：
10.1063/1.531625
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
P. Guha
中科院分区：
文献类型：
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作者：
R. Balakrishnan;P. Guha
将Lund和Regge的表面嵌入性方法应用于经典的非齐次Heisenberg自旋链，研究了一类自旋演化方程及其规范等效广义非线性薛定谔方程（GNLSE）可精确解的非齐次函数f。将自旋向量S（x,t）写成∂xr，并将r（x,t）与生成曲面的位置向量标识，我们证明了r满足的运动学方程暗示了对该曲面的可容许几何的某些约束。这些约束，加上gaas - mainadi - codazzi方程，使我们能够用度规系数G及其导数来表示第二种基本形式的系数和f，对于任意时间无关的G，也可以用相同的量来找到GNLSE的显式解。在由r生成的可容许曲面中，自然出现的一类特殊曲面是旋转曲面：我们找到了r和S的显式解……
The surface‐embeddability approach of Lund and Regge is applied to the classical, inhomogeneous Heisenberg spin chain to study the class of inhomogeneity functions f for which the spin evolution equation and its gauge‐equivalent generalized nonlinear Schrodinger equation (GNLSE) are exactly solvable. Writing the spin vector S(x,t) as ∂xr and identifying r(x,t) with a position vector generating a surface, we show that the kinematic equation satisfied by r implies certain constraints on the admissible geometries of this surface. These constraints, together with the Gauss–Mainardi–Codazzi equations, enable us to express the coefficient of the second fundamental form as well as f in terms of the metric coefficients G and its derivatives, for arbitrary time‐independent G. Explicit solutions for the GNLSE can also be found in terms of the same quantities. Of the admissible surfaces generated by r, a special class that emerges naturally is that of surfaces of revolution: Explicit solutions for r and S are found ...