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

In some recent papers, the so called (H, rho)-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 rho is a certain rule applied periodically on 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 -> O, 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.