We show how the approach to equilibrium in Kirman's ants model can be fully characterized in terms of the spectrum of a Schrödinger equation with a Pöschl–Teller (tan 2 ) potential. Among other interesting properties, we have found that in the bimodal phase where ants visit mostly one food site at a time, the switch time between the two sources only depends on the 'spontaneous conversion' rate and not on the recruitment rate. More complicated correlation functions can be computed exactly, and involve higher and higher eigenvalues and eigenfunctions of the Schrödinger operator, which can be expressed in terms of hypergeometric functions.

中文翻译：

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Schrödinger的蚂蚁：对Kirman招聘模型的连续描述

我们展示了如何利用具有Pöschl–Teller（tan 2）势的Schrödinger方程的频谱来充分表征Kirman蚂蚁模型中的平衡方法。在其他有趣的特性中，我们发现在双峰阶段，蚂蚁一次主要访问一个食物场所，两种来源之间的转换时间仅取决于“自发转换”率，而不取决于招募率。可以精确地计算出更复杂的相关函数，并且包含越来越多的Schrödinger算符的特征值和特征函数，可以用超几何函数表示。