A phenomenological operator description of interactions between populations with applications to migration

TL;DR

This paper introduces an operator-based framework using fermionic operators to model interacting populations and migration phenomena, providing a novel approach that naturally enforces population density limits.

Contribution

It develops a new operatorial method employing fermionic operators for modeling population interactions and migration, improving upon previous models by incorporating natural density bounds.

Findings

The method effectively models diffusion and migration processes.

Fermionic operators impose natural upper bounds on population densities.

The approach offers a flexible framework for analyzing population dynamics.

Abstract

We adopt an operatorial method based on the so-called creation, annihilation and number operators in the description of different systems in which two populations interact and move in a two-dimensional region. In particular, we discuss diffusion processes modeled by a quadratic hamiltonian. This general procedure will be adopted, in particular, in the description of migration phenomena. With respect to our previous analogous results, we use here fermionic operators since they automatically implement an upper bound for the population densities.