海森堡模型中能级的有序化及其应用
Ordering of Energy Levels in Heisenberg Models and Applications
摘要：
在最近的一篇论文中，我们证明了对于铁磁海森堡模型，固定总自旋不变子空间中的最小本征值是随总自旋单调递减的，我们称这种性质为铁磁能级序（FOEL）。我们对链上具有任意自旋和耦合常数的海森堡模型证明了这个猜想。在本文中，我们给出了一个教学介绍，这一结果，并讨论了一些扩展和影响。后者包括的性质，对称简单的排斥过程的松弛时间的图，其中FOEL可以证明，等于松弛时间的随机游走在同一个图。这种弛豫时间的相等性被称为Aldous猜想。
英文摘要：
In a recent paper we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin and called this property ferromagnetic ordering of energy levels (FOEL). We have proved this conjecture for the Heisenberg model with arbitrary spins and coupling constants on a chain. In this paper we give a pedagogical introduction to this result and also discuss some extensions and implications. The latter include the property that the relaxation time of symmetric simple exclusion processes on a graph for which FOEL can be proved, equals the relaxation time of a random walk on the same graph. This equality of relaxation times is known as Aldous' Conjecture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
