Dynamics with Asymptotic Equilibria

This chapter, even considering a rather simple model, illustrates the (H, ρ) -induced dynamics approach, where H denotes the Hamiltonian for a system S, while ρ is a certain rule acting at specific times kτ (k integer and τ fixed), by modifying some of the parameters entering H according to the state variation of the system itself; the most important effect is that the dynamics approaches some asymptotic equilibrium state. We also 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 initial parameters involved in the Hamiltonian to the asymptotic equilibrium states.