Schrödinger’s ants: a continuous description of Kirman’s recruitment model

Author: 

Moran, J
Fosset, A
Benzaquen, M
Bouchaud, J

Publication Date: 

4 August 2020

Journal: 

Journal of Physics: Complexity

Last Updated: 

2021-07-26T06:37:04.097+01:00

Issue: 

3

Volume: 

1

DOI: 

10.1088/2632-072x/aba115

page: 

035002-035002

abstract: 

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 (tan2) 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.

Symplectic id: 

1145385

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article