The Generalized SIC-OEP formalism and the Generalized SIC-Slater approximation (stationary and time-dependent cases)

We present a generalized formulation of the Optimized Effective Potential (OEP) approach to the Self Interaction Correction (SIC) problem in Time Dependent (TD) Density Functional Theory (DFT). The formulation relies on the introduction of a double set of single electron orbitals. It allows the derivation of a generalized Slater approximation to the full OEP formulation, which extends the domain of validity of the standard Slater approximation. We discuss both formal aspects and practical applications of the new formalism and give illustrations in cluster and molecules. The new formalism provides a valuable ansatz to more elaborate (and computationally very demanding) full TD OEP and full TD SIC calculations especially in the linear domain

Generalization of internal Density Functional Theory and Kohn-Sham scheme to multicomponent systems, and link with traditional DFT

We generalize the recently developped "internal" Density Functional Theory (DFT) and Kohn-Sham scheme to multicomponent systems. We obtain a general formalism, applicable for the description of multicomponent self-bound systems (as molecules where the nuclei are treated explicitely, atomic nuclei and mix of 3He and 4He droplets), where the fundamental translational symmetry has been treated correctly. The main difference with traditional DFT is the explicit inclusion of center-of-mass correlations in the functional. A large part of the paper is dedicated to the application to molecules, which permits among other to clarify the approximations that underly traditional DFT.Comment: 20 pages, 46 reference

Time-dependent Internal DFT formalism and Kohn-Sham scheme

We generalize to the time-dependent case the stationary Internal DFT / Kohn-Sham formalism presented in Ref. [14]. We prove that, in the time-dependent case, the internal properties of a self-bound system (as an atomic nuclei) are all defined by the internal one-body density and the initial state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way to compute the internal density. The main difference with the traditional DFT / Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the functional.Comment: 13 pages. To be published in Phys. Rev.

A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform

We consider the high-resolution seismic imaging method called full-waveform inversion (FWI). FWI is a data fitting method aimed at inverting for subsurface mechanical parameters. Despite the large adoption of FWI by the academic and industrial communities, and many successful results, FWI still suffers from severe limitations. From a mathematical standpoint, FWI is a large scale PDE-constrained optimization problem. The misfit function that is used, which measures the discrepancy between observed seismic data and data calculated through the solution of a wave propagation problem, is non-convex. After discretization, the size of the FWI problem requires the use of local optimization solvers, which are prone to converge towards local minima. Thus the success of FWI strongly depends on the choice of the initial model to ensure the convergence towards the global minimum of the misfit function. This limitation has been the motivation for a large variety of strategies. Among the different methods that have been investigated, the use of optimal transport (OT) distances-based misfit functions has been recently promoted. The leading idea is to benefit from the inherent convexity of OT distances with respect to dilation and translation to render the FWI problem more convex. However, the application of OT distances in the framework of FWI is not straightforward, as seismic data is signed, while OT has been developed for the comparison of probability measures. The purpose of this study is to review two methods that were developed to overcome this difficulty. Both have been successfully applied to field data in an industrial framework. Both make it possible to better exploit the seismic data, alleviating the sensitivity to the initial model and to various conventional workflow steps, and reducing the uncertainty attached to the subsurface mechanical parameters inversion.Comment: 18 figure

Polarizibilities as a test of localized approximations to the self-interaction correction

We present applications of the recently introduced ``Generalized SIC-Slater'' scheme which provides a simple Self-Interaction Correction approximation in the framework of the Optimized Effective Potential. We focus on the computation of static polarizabilities which are known to constitute stringent tests for Density Functional Theory. We apply the new method to model H chains, but also to more realistic systems such as C4 (organic) chains, and less symmetrical systems such as a Na5 (metallic) cluster. Comparison is made with other SIC schemes, especially with the standard SIC-Slater one.Comment: 17 pages, 4 figures, 49 reference