论文标题
Schrödinger'sAnt：对Kirman招聘模型的连续描述
Schrödinger's ants: A continuous description of Kirman's recruitment model
论文作者
论文摘要
我们展示了如何通过Pöschl-Teller（$ \ tan^2 $）电位的Schrödinger方程的光谱来充分表征Kirman Ants模型中平衡方法。 Among other interesting properties, we have found that in the bimodal phase where ants visit mostly one food site at a time, the switch time between the two sources only depends on the ``spontaneous conversion" rate and not on the recruitment rate. More complicated correlation functions can be computed exactly, and involve higher and higher eigenvalues and eigenfunctions of the Schrödinger operator, which can be expressed in terms of超几何功能。
We show how the approach to equilibrium in Kirman's ants model can be fully characterized in terms of the spectrum of a Schrödinger equation with a Pöschl-Teller ($\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.
