Time-dependent occupation numbers in reduced-density-matrix functional theory: Application to an interacting Landau-Zener model

We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.Comment: 6 pages, revised, Fig. 2 adde

Many body effects in the excitation spectrum of a defect in SiC

We show that electron correlations control the photophysics of defects in SiC through both renormalization of the quasiparticle bandstructure and exciton effects. We consider the carbon vacancy, which is a well-identified defect with two possible excitation channels that involve conduction and valence band states. Corrections to the Kohn-Sham ionization levels are found to strongly depend on the occupation of the defect state. Excitonic effects introduce a red shift of 0.23 eV. The analysis unambigiously re-assigns excitation mechanism at the thresholds in photo-induced paramagnetic resonance measurements [J. Dashdorj \emph{et al.}, J. Appl. Phys. \textbf{104}, 113707 (2008)]

General formalism for the efficient calculation of derivatives of EM frequency-domain responses and derivatives of the misfit

Electromagnetic (EM) studies of the Earth have advanced significantly over the past few years. This progress was driven, in particular, by new developments in the methods of 3-D inversion of EM data. Due to the large scale of the 3-D EM inverse problems, iterative gradient-type methods have mostly been employed. In these methods one has to calculate multiple times the gradient of the penalty function—a sum of misfit and regularization terms—with respect to the model parameters. However, even with modern computational capabilities the straightforward calculation of the misfit gradients based on numerical differentiation is extremely time consuming. Much more efficient and elegant way to calculate the gradient of the misfit is provided by the so-called ‘adjoint' approach. This is now widely used in many 3-D numerical schemes for inverting EM data of different types and origin. It allows the calculation of the misfit gradient for the price of only a few additional forward calculations. In spite of its popularity we did not find in the literature any general description of the approach, which would allow researchers to apply this methodology in a straightforward manner to their scenario of interest. In the paper, we present formalism for the efficient calculation of the derivatives of EM frequency-domain responses and the derivatives of the misfit with respect to variations of 3-D isotropic/anisotropic conductivity. The approach is rather general; it works with single-site responses, multisite responses and responses that include spatial derivatives of EM field. The formalism also allows for various types of parametrization of the 3-D conductivity distribution. Using this methodology one can readily obtain appropriate formulae for the specific sounding methods. To illustrate the concept we provide such formulae for a number of EM techniques: geomagnetic depth sounding (GDS), conventional and generalized magnetotellurics, the magnetovariational method, horizontal gradient sounding (HGS) and a method that combines HGS with GDS. We also show how the developed formalism can be adapted for the inversion of multisite responses—horizontal magnetic and electric tensor

General formalism for the efficient calculation of the Hessian matrix of EM data misfit and Hessian-vector products based upon adjoint sources approach

3-D electromagnetic (EM) studies of the Earth have advanced significantly over the past decade. Despite a certain success of the 3-D EM inversions of real data sets, the quantitative assessment of the recovered models is still a challenging problem. It is known that one can gain valuable information about model uncertainties from the analysis of Hessian matrix. However, even with modern computational capabilities the calculation of the Hessian matrix based on numerical differentiation is extremely time consuming. Much more efficient way to compute the Hessian matrix is provided by an ‘adjoint sources' methodology. The computation of Hessian matrix (and Hessian-vector products) using adjoint formulation is now well-established approach, especially in seismic inverse modelling. As for EM inverse modelling we did not find in the literature a description of the approach, which would allow EM researchers to apply this methodology in a straightforward manner to their scenario of interest. In the paper, we present formalism for the efficient calculation of the Hessian matrix using adjoint sources approach. We also show how this technique can be implemented to calculate multiple Hessian-vector products very efficiently. The formalism is general in the sense that it allows to work with responses that arise in EM problem set-ups either with natural- or controlled-source excitations. The formalism allows for various types of parametrization of the 3-D conductivity distribution. Using this methodology one can readily obtain appropriate formulae for the specific sounding methods. To illustrate the concept we provide such formulae for two EM techniques: magnetotellurics and controlled-source sounding with vertical magnetic dipole as a sourc

On processing of Controlled Source Electromagnetic (CSEM) Data

In this paper, we present a fast and robust scheme of controlled source electromagnetic data processing. We specify in detail various types of noise that affect measurements and show how these noise components can be suppressed. We promote an improved algorithm to process noisy data. We demonstrate that our method can recover response functions from extremely noisy field data. The proposed software can be adapted to new data sets and noisy environments. We apply our processing method to field data from Kola Peninsula, Norilsk region and Pechora province (Russia)