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

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

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.

Suggested Citation

  • Bagarello, F. & Di Salvo, R. & Gargano, F. & Oliveri, F., 2018. "(H,ρ)-induced dynamics and large time behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 355-373.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:355-373
    DOI: 10.1016/j.physa.2018.03.090
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    References listed on IDEAS

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    1. Khrennikova, Polina, 2016. "Application of quantum master equation for long-term prognosis of asset-prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 253-263.
    2. Bagarello, F. & Gargano, F., 2017. "Modeling interactions between political parties and electors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 243-264.
    3. Bagarello, Fabio & Oliveri, Francesco, 2014. "Dynamics of closed ecosystems described by operators," Ecological Modelling, Elsevier, vol. 275(C), pages 89-99.
    4. Bagarello, F. & Haven, E., 2016. "First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 403-414.
    5. Asano, Masanari & Basieva, Irina & Khrennikov, Andrei & Ohya, Masanori & Tanaka, Yoshiharu, 2012. "Quantum-like dynamics of decision-making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2083-2099.
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    Cited by:

    1. Di Salvo, Rosa & Gorgone, Matteo & Oliveri, Francesco, 2020. "Generalized Hamiltonian for a two-mode fermionic model and asymptotic equilibria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Bagarello, F., 2020. "One-directional quantum mechanical dynamics and an application to decision making," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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