论文标题
对称正交多项式的新家族和动力学链的可解决模型
New family of symmetric orthogonal polynomials and a solvable model of a kinetic spin chain
论文作者
论文摘要
我们研究一个无限的一维iSing自旋链，每个粒子仅与其最近的邻居相互作用，并与热浴接触，温度沿链条质量衰减。磁化（自旋期望值）的时间演变由半侵犯的Jacobi矩阵控制。矩阵属于雅各比矩阵的三参数家族，其光谱问题证明可以解决基本的高几幅序列。结果，我们推断出相应的正交多项式的基本特性，这似乎是新的。最后，我们返回ISING模型，研究磁化和两旋相关性的时间演变。
We study an infinite one-dimensional Ising spin chain where each particle interacts only with its nearest neighbors and is in contact with a heat bath with temperature decaying hyperbolically along the chain. The time evolution of the magnetization (spin expectation value) is governed by a semi-infinite Jacobi matrix. The matrix belongs to a three-parameter family of Jacobi matrices whose spectral problem turns out to be solvable in terms of the basic hypergeometric series. As a consequence, we deduce the essential properties of the corresponding orthogonal polynomials, which seem to be new. Finally, we return to the Ising model and study the time evolution of magnetization and two-spin correlations.
