Understanding the behavior of many electrons in interaction is one of the greatest challenges of modern quantum physics, called the quantum N-body problem. Part of the issue for describing the quantum behavior of the electronic density comes from the description of excitations in a system. Formally, the description of excited states can be understood as coupling in time, i.e. the history-dependence of materials properties, also called non-adiabatic effects. These can show up in the most diverse manner, such as satellites in photoemission spectra of solids or double excitation in molecules. Non-adiabatic effects are at the origin of phenomena that enter modern technologies, such as charge migration and multiple exciton generation, that is a promise for photovoltaic applications.
From the theoretical point of view, a full description of the N-electron system would ask for the solution of the full Schrödinger equation, which is not feasible for more than a few electrons. In practice, the full wave function contains much more information than the observables of interest.
One way to circumvent this issue is to focus on compact quantities (electronic density, density matrix, one-body Green's function, spectral function, etc.) to develop functionals that simplify calculations and make them tractable for realistic systems.
Most approximations used to compute these reduced quantities have strong limitations concerning these non-adiabatic effects. For example, in quantum chemistry, a lot of work focuses on the electronic density as the reduced quantity and the method of choice to describe excited states is the Time-Dependent Density Functional Theory (TDDFT), where most functionals are purely adiabatic. In solids, the one-body Green’s function computed within the GW approximation is the standard. Green's function methods rapidly meet their limits when it comes to the description of non-adiabatic coupling between excitations. For instance, GW approximation to the electron self-energy is not able to well describe plasmon satellites that are observed in photoemission spectra. Also, because Green’s functions are a bigger object than the density, Green's functions-based approaches would mostly require a computational effort that is still out of reach in many systems.
In this project, the philosophy is to use data on precomputed model systems and explore various reduced quantities to retrieve non-adiabatic effects. The overall objective is to advance the understanding and prediction of non-adiabatic effects in materials and spectroscopies, in order to identify novel phenomena and enhance theoretical frameworks.
