The temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g. Density-Functional Theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak's theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak's theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principle context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the Density-Functional Perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion terms. For the two different numerical approaches without rigid-ion terms, the agreement is better than 7 $\mu$eV in the case of diamond, which represent an agreement to 5 significant digits. The magnitude of the non rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies

Pour mémoire – François Chappé

Il est parti le 18 novembre 2007. Insolite personnage, insolite cérémonie, toute entière voulue par François Chappé et demandée dans son testament, insolite photographie, prise lors d’un cours public organisé en plein air, devant l’Université, entre les deux tours de l’élection présidentielle de 2002. Un cours d’histoire contemporaine sur la montée des fascismes. Un cours ouvert à tous, syndicalistes, républicains, démocrates. Étudiants, bien sûr. Cette photo qu’il nous a demandé de retenir ..

Reconstruction of source location in a network of gravitational wave interferometric detectors

This paper deals with the reconstruction of the direction of a gravitational wave source using the detection made by a network of interferometric detectors, mainly the LIGO and Virgo detectors. We suppose that an event has been seen in coincidence using a filter applied on the three detector data streams. Using the arrival time (and its associated error) of the gravitational signal in each detector, the direction of the source in the sky is computed using a chi^2 minimization technique. For reasonably large signals (SNR>4.5 in all detectors), the mean angular error between the real location and the reconstructed one is about 1 degree. We also investigate the effect of the network geometry assuming the same angular response for all interferometric detectors. It appears that the reconstruction quality is not uniform over the sky and is degraded when the source approaches the plane defined by the three detectors. Adding at least one other detector to the LIGO-Virgo network reduces the blind regions and in the case of 6 detectors, a precision less than 1 degree on the source direction can be reached for 99% of the sky.Comment: Accepted in Phys. Rev.