The central goal in quantum scattering theory is to classify asymptotic states, describing the possible long-time behaviors of solutions, and to prove that all solutions converge to a superposition of these asymptotic states—a concept known as asymptotic completeness (AC). Historically, local decay estimates (LD) have played a crucial role in proving AC. In this talk, we will focus on Schr\”odinger equations. I will present a method for proving AC without relying on LD and introduce an approach to establish LD using AC. As an application, we obtain global-in-time Strichartz estimates for Schr\”odinger equations with time-quasi-periodic potentials. This work is based on joint research with Avy Soffer.