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

Francesco Gargano, Fabio Bagarello, Bagarello, Di Salvo, Francesco Oliveri

Risultato della ricerca: Article

6 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)355-373
Numero di pagine19
RivistaPHYSICA. A
Volume505
Stato di pubblicazionePublished - 2018

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cita questo

Gargano, F., Bagarello, F., Bagarello, Di Salvo, & Oliveri, F. (2018). (H,ρ)-induced dynamics and large time behaviors. PHYSICA. A, 505, 355-373.