Density-potential mapping in the standard and quantum electrodynamical time-dependent density functional theory

This thesis is devoted to the formulation and implications of the time-dependent density functional theory (TDDFT). The work is divided into two main parts. In the first part we develop rigorous theorems for the density-potential mapping in quantum many-body systems on a lattice. We prove the uniqueness of the TDDFT map and demonstrate that a given density is v-representable if the initial many-body state and the density satisfy certain well defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is v-representable. Then the lattice TDDFT formulation is extended to cover system of interacting lattice electrons strongly coupled to cavity photons.We prove that under some mathematical conditions the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate. Then we further generalize the ground state v representability theorem to include the ground state of a general lattice electron-photon Hamiltonian.I appreciate the financial support from >Grupos Consolidados UPV/EHU del Gobierno Vasco>, >MEC y MICINN>, Ikerbasque foundation of science and the Air Force Office of Scientific Research.Peer Reviewe

The time-dependent exchange-correlation functional for a Hubbard dimer: quantifying non-adiabatic effect

We address and quantify the role of non-adiabaticity ("memory effects") in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing non-linear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong non-linear and non-adiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble 2-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, (ii) there is a sizable non-adiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground state population is dominant. We then propose a "two-level" approximation for the time-dependent xc potential which can capture Rabi dynamics in the 2-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime. This new, fully non-adiabatic and explicit density functional constitutes one of the main results of the present work.Comment: 8 pages, 5 figure

Predicting entity mentions in scientific literature

Predicting which entities are likely to be mentioned in scientific articles is a task with significant academic and commercial value. For instance, it can lead to monetary savings if the articles are behind paywalls, or be used to recommend articles that are not yet available. Despite extensive prior work on entity prediction in Web documents, the peculiarities of scientific literature make it a unique scenario for this task. In this paper, we present an approach that uses a neural network to predict whether the (unseen) body of an article contains entities defined in domain-specific knowledge bases (KBs). The network uses features from the abstracts and the KB, and it is trained using open-access articles and authors’ prior works. Our experiments on biomedical literature show that our method is able to predict subsets of entities with high accuracy. As far as we know, our method is the first of its kind and is currently used in several commercial settings