Effective Models for Non-equilibrium Dynamics

Understanding and predicting ultrafast, driven phenomena and the emergence of dynamical correlations in materials require theoretical frameworks that integrate many-body theory, real-time dynamics, and open-quantum-system approaches on femtosecond timescales. Practical theoretical treatments require developing an effective representation of the problem (via downfolded models )and extracting the relevant quantities, typically the correlation functions. In this talk, I will discuss recent developments in non-equilibrium dynamics based on single- and two-particle Green's function evolution, formulated as a downfolded description of electronic structure dynamics. Building on this foundation, I will introduce a Lindblad-type embedding that extends Green's function methods to open quantum systems. Together, these developments establish a framework for constructing improvable, ab initio–based effective models that reliably capture ultrafast energy flow, quasiparticle renormalization, and excitonic dynamics in complex materials.