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Generalized Hamiltonian for a two-mode fermionic model and asymptotic equilibria

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  • Di Salvo, Rosa
  • Gorgone, Matteo
  • Oliveri, Francesco

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, has been introduced. According to the formal mathematical apparatus of quantum mechanics, H denotes the Hamiltonian for S, while ρ is a certain rule applied periodically on S. In this approach the rule acts at specific times kτ, with k integer and τ fixed, by modifying some of the parameters entering H according to the state variation of the system. As a result, a dynamics admitting an asymptotic equilibrium state can be obtained. Here, we consider the limit for τ→0, so that we introduce a generalized model leading to asymptotic equilibria. Moreover, in the case of a two-mode fermionic model, we are able to derive a relation linking the parameters involved in the Hamiltonian to the asymptotic equilibrium states.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317108
    DOI: 10.1016/j.physa.2019.123032
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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.
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    6. 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.
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