On fermionic models of a closed ecosystem with application to bacterial populations

Abstract

This paper deals with the application of operatorial techniques of quantum physics to a theoretical model of closed ecosystems. The model is built by using fermionic operators whose evolution is ruled by a self--adjoint Hamiltonian operator. Adopting Heisenberg--like dynamics, we consider either linear or nonlinear models with the aim of describing the long-term survival of bacterial populations; the introduction of effective dissipative mechanisms is also considered. Moreover, a variant of linear models through the introduction of additional rules acting periodically on the system is proposed. Specifically, the evolution in a time interval is obtained by gluing the evolutions in a finite set of adjacent subintervals. In each subinterval the Hamiltonian is time independent, but the values of the parameters entering the Hamiltonian may be changed by the rules at the end of a subinterval on the basis of the actual state of the system. Within this context, a new approach is provided in order to obtain reliable results, without increasing the computational cost of the numerical integration of the differential equations involved.