Operatorial formulation of crimo-taxis phenomena in a street

• URL: http://arxiv.org/abs/2504.13930v1
• Date: Mon, 14 Apr 2025 17:03:13 GMT
• Title: Operatorial formulation of crimo-taxis phenomena in a street
• Authors: M. Gorgone, G. Inferrera, C. F. Munafo',
• Abstract summary: In this paper, the ladder operators typical of quantum mechanics are used to construct an operatorial version of a model dubbed crimo-taxis.<n>In a classical framework, the crimo-taxis model is described by reaction-diffusion partial differential equations.<n>The results of some numerical simulations in a one-dimensional setting are presented and discussed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, the ladder operators typical of quantum mechanics are used to construct an operatorial version of a model dubbed crimo-taxis. In a classical framework, the crimo-taxis model is described by reaction-diffusion partial differential equations describing a population divided into three interacting subgroups (ordinary citizens, drug users/dealers, and law enforcement personnel). By means of a quantum-like approach, these interacting subgroups are modeled using annihilation, creation, and number fermionic operators. Their dynamics is governed by a self-adjoint and time-independent Hamiltonian operator, emboding the interactions among the groups. Furthermore, a recent variant of the standard Heisenberg approach, namely $(\mathcal{H},\rho)$--induced dynamics, is also taken into account with the goal of enriching the dynamics. The results of some numerical simulations in a one--dimensional setting are presented and discussed.

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