Operatorial formulation of crimo-taxis phenomena in a street

In this paper, the ladder operators and a quantum-like approach are used to construct an operatorial version of a model dubbed crimo-taxis. In a classical framework, the crimo-taxis model is represented by reaction-diffusion partial differential equations that describe a population divided into three interacting subgroups (ordinary citizens, drug users/dealers, and law enforcement personnel) living in a one-dimensional spatial region representing a street. In this new framework, the agents of the subgroups are modeled using annihilation, creation, and number fermionic operators, and their time evolution is assumed to be ruled by a Hermitian time-independent Hamiltonian operator suitable to capture the interactions among the subgroups. Furthermore, a recent extension of the standard Heisenberg view, namely ( H , ρ ) -induced dynamics, is also taken into account. Two scenarios, characterized by different initial spatial distributions of the subgroups, are considered. The results of some numerical simulations in a one-dimensional setting are presented and discussed.