Search results for " Fermionic operators"
showing 4 items of 4 documents
A PHENOMENOLOGICAL OPERATOR DESCRIPTION OF INTERACTIONS BETWEEN POPULATIONS WITH APPLICATIONS TO MIGRATION
2013
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.
An operatorial description of desertification
2016
We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. Each actor is described by a time dependent fermionic operator, and the dynamics is ruled by a self-adjoint Hamilton-like operator. We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes. We first describe the simplified model in one cell. Then, we define the full model on a two-dimensional region, taking into account additional…
(H, ρ)-induced dynamics and the quantum game of life
2017
Abstract We propose an extended version of quantum dynamics for a certain system S , whose evolution is ruled by a Hamiltonian H, its initial conditions, and a suitable set ρ of rules, acting repeatedly on S . The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of H, ρ as well as on the initial conditions. After a general discussion on this (H, ρ)-induced dynamics, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension.
Dynamics of closed ecosystems described by operators
2014
Abstract We adopt the so-called occupation number representation , originally used in quantum mechanics and recently adopted in the description of several classical systems, in the analysis of the dynamics of some models of closed ecosystems. In particular, we discuss two linear models, for which the solution can be found analytically, and a nonlinear system, for which we produce numerical results. We also discuss how a dissipative effect could be effectively implemented in the model.