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

Abstract

In some recent papers, the so called $(H,\rho )$-induced dynamics of a system $\mathcal{S}$ 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 $\mathcal{S}$, while $\rho$ is a certain rule applied periodically on $\mathcal{S}$. In this approach the rule acts at specific times $k\tau$, with $k$ integer and $\tau$ 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 $\tau \to 0$, 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.

26 pages, 31 figures. arXiv admin note: text overlap with arXiv:1803.11234

References in corpus (4)

• An operatorial approach to stock markets
• A Phenomenological Operator Description of Dynamics of Crowds: Escape Strategies
• $(H,\rho )$--induced political dynamics: facets of the disloyal attitudes into the public opinion
• Political dynamics affected by turncoats