Week 11.05.2026 – 17.05.2026

Although time is continuous, many physical processes and models are either constructed with a discrete time variable, or require time discretization to be tractable. While Markovian processes in discrete time have been studied in great details over many decades, memory effects induced by hidden degrees of freedom remain greatly unexplored in discrete-time dynamics. In this talk, I will focus on the general case where the evolution of the system state after n time steps depends on all its previous states in a linear way. In particular, I will identify a well-delineated regime where the dynamics can be faithfully approximated by a Markovian-like, first-order recurrence relation. This regime is defined through strict inequalities rather than comparison of orders of magnitude, as is often the case when justifying memoryless approximations. I will show how this formalism can be applied in concrete examples -- both quantum and classical -- and how it paves the way for the derivation of approximations in the strong-memory regime and for systems with periodic driving.