Description of nuclear systems with a self-consistent configuration-mixing approach. I: Theory, algorithm, and application to the 12^{12}C test nucleus

Although self-consistent multi-configuration methods have been used for decades to address the description of atomic and molecular many-body systems, only a few trials have been made in the context of nuclear structure. This work aims at the development of such an approach to describe in a unified way various types of correlations in nuclei, in a self-consistent manner where the mean-field is improved as correlations are introduced. The goal is to reconcile the usually set apart Shell-Model and Self-Consistent Mean-Field methods. This approach is referred as "variational multiparticle-multihole configuration mixing method". It is based on a double variational principle which yields a set of two coupled equations that determine at the same time the expansion coefficients of the many-body wave function and the single particle states. The formalism is derived and discussed in a general context, starting from a three-body Hamiltonian. Links to existing many-body techniques such as the formalism of Green's functions are established. First applications are done using the two-body D1S Gogny effective force. The numerical procedure is tested on the $^{12}$C nucleus in order to study the convergence features of the algorithm in different contexts. Ground state properties as well as single-particle quantities are analyzed, and the description of the first $2^+$ state is examined. This study allows to validate our numerical algorithm and leads to encouraging results. In order to test the method further, we will realize in the second article of this series, a systematic description of more nuclei and observables obtained by applying the newly-developed numerical procedure with the same Gogny force. As raised in the present work, applications of the variational multiparticle-multihole configuration mixing method will however ultimately require the use of an extended and more constrained Gogny force.Comment: 22 pages, 18 figures, accepted for publication in Phys. Rev. C. v2: minor corrections and references adde

High-performance functional renormalization group calculations for interacting fermions

We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the $t$,$t'$ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.Comment: 26 pages, 9 figure

The taxonomic status of the genus <i>Stylactaria</i> Stechow, 1921 (Hydroidomedusae, Anthomedusae, Hydractiniidae), with the description of a new species

The status of all the species ascribed in the literature to Stylactaria is discussed, that nominal genus is considered a congener of Hydractinia and a new species (Hydractinia calderi n. sp.) is described. The medusae of the medusa-based genera Hansiella and Tregoubovia, formerly ascribed to the Hydractiniidae, are shown to be more like the medusae of Thecocodium, a genus having ptilocodiid hydroids. Both Hansiella and Tregoubovia are thus transferred to the Ptilocodiidae.With their removal from the Hydractiniidae, a redefinition of both families is provided. The genus Fiordlandia is considered as synonym of Clavactinia

Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion

The electricity market is a very peculiar market due to the large variety of phenomena that can affect the spot price. However, this market still shows many typical features of other speculative (commodity) markets like, for instance, data clustering and mean reversion. We apply the diffusion entropy analysis (DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting time statistics between consecutive spot price spikes and find it to show anomalous scaling characterized by a decaying power-law. The exponent observed in data follows a quite robust relationship with the one implied by the DEA analysis. We also in terms of the DEA revisit topics like clustering, mean-reversion and periodicities. We finally propose a GARCH inspired model but for the price itself. Models in the context of stochastic volatility processes appear under this scope to have a feasible description.Comment: 16 pages, 7 figure

Site-selective laser spectroscopy of Nd 3+ ions in 0.8CaSiO 3-0.2Ca 3(PO 4) 2 biocompatible eutectic glass-ceramics

In this work we report the influence of the crystallization stage of the host matrix on the spectroscopic properties of Nd3+ ions in biocompatible glass-ceramic eutectic rods of composition 0.8CaSiO3-0.2Ca3(PO4)2 doped with 1 and 2 wt% of Nd2O3. The samples were obtained by the laser floating zone technique at different growth rates between 50 and 500 mm/h. The microstructural analysis shows that a growth rate increase or a rod diameter decrease leads the system to a structural arrangement from three (two crystalline and one amorphous) to two phases (one crystalline and one amorphous). Electron backscattering diffraction analysis shows the presence of Ca2SiO4 and apatite-like crystalline phases. Site-selective laser spectroscopy in the 4I9/2¿4F3/2/4F5/2 transitions confirms that Nd3+ ions are incorporated in crystalline and amorphous phases in these glass-ceramic samples. In particular, the presence of Ca2SiO4 crystalline phase in the samples grown at low rates, which has an excellent in vitro bioactivity, can be unambiguously identified from the excitation spectra and lifetime measurements of the 4F3/2 state of Nd3+ ions

"No-Scalar-Hair" Theorems for Nonminimally Coupled Fields with Quartic Self-Interaction

Self-gravitating scalar fields with nonminimal coupling to gravity and having a quartic self-interaction are considered in the domain of outer communications of a static black hole. It is shown that there is no value of the nonminimal coupling parameter $\zeta$ for which nontrivial static black hole solutions exist. This result establishes the correctness of Bekenstein ``no-scalar-hair'' conjecture for quartic self-interactions.Comment: 8 pages, RevTeX

Segal-Bargmann-Fock modules of monogenic functions

In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.Comment: 11 page