论文标题
计算怪物电位
Counting monster potentials
论文作者
论文摘要
我们研究了Bazhanov-Lukyanov-Zamolodchikov的怪物电势的巨大动量极限，该奇科夫（根据ODE/IM对应关系）应与量子KDV模型的激发状态相对应。 我们证明，这些电势的极点涉及基态潜力的复杂平衡，并根据赫尔米特多项式的沃斯基人的根部表达对渐近性的领先校正。 这使我们可以将$ n $的每个分区与$ n $根的独特怪物潜力相关联，我们计算了频谱。结果，我们证明 - 最多可以使用一些数学技术 - 修复了整数$ n $，带有$ n $ roots的怪物电位数量与$ n $的整数分区的数量相吻合，这是量子$ n $ n $ n $ n $ n $ nsumpace量子空间的量子。在符合ODE/IM对应关系的惊人之中。
We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which -- according to the ODE/IM correspondence -- should correspond to excited states of the Quantum KdV model. We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials. This allows us to associate to each partition of $N$ a unique monster potential with $N$ roots, of which we compute the spectrum. As a consequence, we prove -- up to a few mathematical technicalities -- that, fixed an integer $N$, the number of monster potentials with $N$ roots coincides with the number of integer partitions of $N$, which is the dimension of the level $N$ subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.
