(H,ρ)-induced dynamics and large time behaviors

F. Bagarello, R. Di Salvo, F. Gargano and F. Oliveri

Physica A: Statistical Mechanics and its Applications, 2018, vol. 505, issue C, 355-373

Abstract: In some recent papers, the so called (H,ρ)-induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, H is the Hamiltonian for S, while ρ is a certain rule applied periodically (or not) on S. The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the (H,ρ)-induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of S may converge, for large t, to certain asymptotic values. This cannot be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any Heisenberg dynamics implemented by a suitable hermitian operator H can only give an oscillating behavior. We prove our claims both analytically and numerically for a simple system with two degrees of freedom, and then we apply our general scheme to a model describing a biological system of bacteria living in a two-dimensional lattice, where two different choices of the rule are considered.

Keywords: Operatorial models; Schrödinger and Heisenberg dynamics; (H,ρ)-induced dynamics; Stressed bacterial populations (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:505:y:2018:i:c:p:355-373

DOI: 10.1016/j.physa.2018.03.090

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