Theoretical determination of the Raman spectra of MgSiO3 perovskite and post-perovskite at high pressure

We use the density functional perturbation theory to determine for the first time the pressure evolution of the Raman intensities for a mineral, the two high-pressure structures of MgSiO3 perovskite and post-perovskite. At high pressures, the Raman powder spectra reveals three main peaks for the perovskite structure and one main peak for the post-perovskite structure. Due to the large differences in the spectra of the two phases Raman spectroscopy can be used as a good experimental indication of the phase transition.Comment: 16 pages, submitted to Geophysical Research Letter

On the Synchronizing Probability Function and the Triple Rendezvous Time for Synchronizing Automata

Cerny's conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping three states onto a single one. The second one is the synchronizing probability function of an automaton, a recently introduced tool which reinterprets the synchronizing phenomenon as a two-player game, and allows to obtain optimal strategies through a Linear Program. Our contribution is twofold. First, by coupling two different novel approaches based on the synchronizing probability function and properties of linear programming, we obtain a new upper bound on the triple rendezvous time. Second, by exhibiting a family of counterexamples, we disprove a conjecture on the growth of the synchronizing probability function. We then suggest natural follow-ups towards Cernys conjecture.Comment: A preliminary version of the results has been presented at the conference LATA 2015. The current ArXiv version includes the most recent improvement on the triple rendezvous time upper bound as well as formal proofs of all the result

Berry-phase treatment of the homogeneous electric field perturbation in insulators

A perturbation theory of the static response of insulating crystals to homogeneous electric fields, that combines the modern theory of polarization (MTP) with the variation-perturbation framework is developed, at unrestricted order of perturbation. First, we address conceptual issues related to the definition of such a perturbative approach. In particular, in our definition of an electric-field-dependent energy functional for periodic systems, the position operator appearing in the perturbation term is replaced by a Berry-phase expression, along the lines of the MTP. Moreover, due to the unbound nature of the perturbation, a regularization of the Berry-phase expression for the polarization is needed in order to define a numerically-stable variational procedure. Regularization is achieved by means of discretization, which can be performed either before or after the perturbation expansion. We compare the two possibilities and apply them to a model tight-binding Hamiltonian. Lowest-order as well as generic formulas are presented for the derivatives of the total energy, the normalization condition, the eigenequation, and the Lagrange parameters.Comment: 52 pages + 4 figures; accepted for publication in Physical Review

A Characterization of Completely Reachable Automata

A complete deterministic finite automaton in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize completely reachable automata in terms of certain directed graphs.Comment: 12 pages, 3 figures, submitted to DLT 201

A many-body perturbation theory approach to the electron-phonon interaction with density-functional theory as a starting point

The electron-phonon interaction plays a crucial role in many fields of physics and chemistry. Nevertheless, its actual calculation by means of modern many-body perturbation theory is weakened by the use of model Hamiltonians that are based on parameters difficult to extract from the experiments. Such shortcoming can be bypassed by using density-functional theory to evaluate the electron-phonon scattering amplitudes, phonon frequencies and electronic bare energies. In this work, we discuss how a consistent many-body diagrammatic expansion can be constructed on top of density-functional theory. In that context, the role played by screening and self-consistency when all the components of the electron-nucleus and nucleus-nucleus interactions are taken into account is paramount. A way to avoid over-screening is notably presented. Finally, we derive cancellations rules as well as internal consistency constraints in order to draw a clear, sound and practical scheme to merge many-body perturbation and density-functional theory.Comment: 25 pages, 13 figure

Excitation energies from density functional perturbation theory

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the ground state and excited states in first-order perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are compared to the excitations obtained within $\Delta$SCF and time-dependent density functional theory. We also calculate the excitation energies in perturbation theory using approximate functionals such as the local density approximation and the optimized effective potential method with and without the Colle-Salvetti correlation contribution

The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a ${\cal O} (1/q^2)$ divergence in the XC kernel for small vectors q. This behaviour, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described as a KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semi-local or even non-local approximations to KS theory. We also show that the test-charge and electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations

Density-operator theory of orbital magnetic susceptibility in periodic insulators

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose, for insulators, a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple, formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.Comment: 5 pages including 2 figures; accepted for publication in Phys. Rev.

A Note on a Recent Attempt to Improve the Pin-Frankl Bound

We provide a counterexample to a lemma used in a recent tentative improvement of the the Pin-Frankl bound for synchronizing automata. This example naturally leads us to formulate an open question, whose answer could fix the line of proof, and improve the bound.Comment: Short note presenting a counterexample and the resulting open questio