Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part I.

Non parametric and parametric estimation for the spectral density of a stationary process is a well-known topic, except when the spectrum vanishes for some frequency. Indeed, for this frequency, the limit law degenerates, and traditional inference no longer applies. The paper introduces non parametric tests of this hypothesis, which exploit the asymptotic behavior of the periodigram for some well-chosen sequence of frequencies.Stationarity ; Spectral density ; Moving average unit root ; Non parametric tests

Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part II.

It is well-known that traditional inference do not apply when the spectral density of a stationary process vanishes for some frequency. This paper examines some properties of several new non parametric tests of this hypothesis which have been recently proposed by Lacroix (1999). These tests exploit the asymptotic behavior of the periodigram for some well-chosen sequence of frequencies. In particular, we investigate the power properties of the tests from both theoretical and empirical approach.Stationarity ; Spectral density ; Moving average unit root ; Non parametric tests.

Thermodynamics of small superconductors with fixed particle number

The Variation After Projection approach is applied for the first time to the pairing hamiltonian to describe the thermodynamics of small systems with fixed particle number. The minimization of the free energy is made by a direct diagonalization of the entropy. The Variation After Projection applied at finite temperature provides a perfect reproduction of the exact canonical properties of odd or even systems from very low to high temperature.Comment: 4 pages, 3 figure

Pair-transfer probability in open- and closed-shell Sn isotopes

Approximations made to estimate two-nucleon transfer probabilities in ground-state to ground-state transitions and physical interpretation of these probabilities are discussed. Probabilities are often calculated by approximating both ground states, of the initial nucleus A and of the final nucleus A\pm 2 by the same quasiparticle vacuum. We analyze two improvements of this approach. First, the effect of using two different ground states with average numbers of particles A and A\pm2 is quantified. Second, by using projection techniques, the role of particle number restoration is analyzed. Our analysis shows that the improved treatment plays a role close to magicity, leading to an enhancement of the pair-transfer probability. In mid-shell regions, part of the error made by approximating the initial and final ground states by a single vacuum is compensated by projecting onto good particle number. Surface effects are analyzed by using pairing interactions with a different volume-to-surface mixing. Finally, a simple expression of the pair-transfer probability is given in terms of occupation probabilities in the canonical basis. We show that, in the canonical basis formulation, surface effects which are visible in the transfer probability are related to the fragmentation of single-particle occupancies close to the Fermi energy. This provides a complementary interpretation with respect to the standard quasiparticle representation where surface effects are generated by the integrated radial profiles of the contributing wave functions.Comment: 12 pages, 7 figure

Energy dependence of nucleus-nucleus potential close to the Coulomb barrier

The nucleus-nucleus interaction potentials in heavy-ion fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory for mass symmetric reactions $^{16}$O${}+^{16}$O, $^{40}$Ca${}+^{40}$Ca, $^{48}$Ca${}+^{48}$Ca and mass asymmetric reactions $^{16}$O$+^{40,48}$Ca, $^{40}$Ca${}+^{48}$Ca, $^{16}$O+$^{208}$Pb, $^{40}$Ca+$^{90}$Zr. When the center-of-mass energy is much higher than the Coulomb barrier energy, potentials deduced with the microscopic theory identify with the frozen density approximation. As the center-of-mass energy decreases and approaches the Coulomb barrier, potentials become energy dependent. This dependence signs dynamical reorganization of internal degrees of freedom and leads to a reduction of the "apparent" barrier felt by the two nuclei during fusion of the order of $2-3$ compared to the frozen density case. Several examples illustrate that the potential landscape changes rapidly when the center-of-mass energy is in the vicinity of the Coulomb barrier energy. The energy dependence is expected to have a significant role on fusion around the Coulomb barrier.Comment: 11 pages, 13 figures, 1 table, discussion of effects of coordinate-dependent mass added, accepted for publication in Phys. Rev.

Static and dynamic study of metal salt hydrates of weakly-coordinating fluoroanions by vibrational spectroscopy, gravimetry, and an analysis of previously published x-ray structures

2021 Spring.Includes bibliographical references.Eighteen metal salt hydrates (Li(H2O)4(Al(OC(CF3)3)4), Li(H2O)(B(3,5-C6H3(CF3)2)4), Li(H2O)n(Ga(C2F5)4), Li(H2O)(PF6), Na(H2O)(PF6), Li2(H2O)4(B12F12), Na2(H2O)2(B12F12), K2(H2O)2(B12F12), Rb2(H2O)2(B12F12), Cs2(H2O)(B12F12), Mg(H2O)6(B12F12), Ca(H2O)n(B12F12), Sr(H2O)n(B12F12), Ba(H2O)n(B12F12), Co(H2O)6(B12F12), Ni(H2O)6(B12F12), Zn(H2O)6(B12F12), and Li2(H2O)2(TiF6)) containing weakly coordinating anions were analyzed using room temperature ATR-FTIR spectroscopy. The goal was to investigate the relative strengths of water–anion hydrogen bonds in the solid-state. In all but one case, these hydrogen bonds take the form of O–H···F hydrogen bonds. The one exception is in the salt Li2(H2O)4(B12F12) where there are both O–H···F and O–H···O hydrogen bonds present. Based on the magnitude of the redshift of the ν(OH) band(s) a qualitative scale for the comparison of the relative hydrogen bond strength is constructed. Included in this scale are additional metal salt hydrates taken from the literature. This spectroscopic study has produced some of the only room temperature spectra for water participating in hydrogen bonding in the solid-state where the νasym(OH) and νsym(OH) bands are individually resolvable. The weak nature of the O–H···F hydrogen bonds allows for resolution of ν(OH) bands only 5 cm−1 apart in some cases. The two metal salt hydrates (Li(H2O)4(Al(OC(CF3)3)4) and Li(H2O)(B(3,5-C6H3(CF3)2)4) are shown to possess the weakest O–H···F hydrogen bonds observed in the solid state at room temperature. The salt Li2(H2O)4(B12F12) contains a cyclic (H2O)4 water cluster, also known as the R4 cluster, is presented, and discussed in the context of the FTIR spectrum of water clusters. Due to the nature of the weak O–H···F hydrogen bonding between the cluster and the surrounding anions the E and B fundamental vibrations for the cluster were able to be determined. The peak-to-peak separation, and relative intensities of these two bands are consistent with computational results from the literature. This is the first time that the R4 water cluster has been successfully studied via FTIR spectroscopy without the presence of other clusters leading to ambiguity in the results. Finally, direct observation of the effect of cation acidity on the relative strength of water–anion hydrogen bonding has been directly observed for the first time in the metal hexahydrate salts M(H2O)6(B12F12) (M = Mg, Co, Ni, Zn). These results, along with the correlation curves constructed in this work, show that it is not possible to assign relative hydrogen bond strength based on O–H···X bond length, nor is it possible to accurately approximate O–H···X bond length based on degree of ν(OH) redshift. Instead, it is shown that the relative basicity of the anion is the primary factor governing the relative hydrogen bond strength, and thus the degree of redshifting experienced by the ν(OH) band(s). The cation acidity also is shown to have a lesser, but observable, effect on the relative strength of O–H···X hydrogen bond. In addition to broadening our fundamental understanding of hydrogen bonding in the solid state, this work also shows that FTIR spectroscopy can be a useful tool for rapidly assigning relative basicity of new weakly coordinating anions without need the for complex protonation experiments

Magnetic blackbody shift of hyperfine transitions for atomic clocks

We derive an expression for the magnetic blackbody shift of hyperfine transitions such as the cesium primary reference transition which defines the second. The shift is found to be a complicated function of temperature, and has a T^2 dependence only in the high-temperature limit. We also calculate the shift of ground-state p_1/2 hyperfine transitions which have been proposed as new atomic clock transitions. In this case interaction with the p_3/2 fine-structure multiplet may be the dominant effect

Analyse conjoncturelle de données brutes et estimation de cycles Partie 1 : estimation et tests.

Short-term analysis is generally performed with seasonally adjusted data from which further estimation of the business cycle is performed through well-known filters (HP, Baxter-King). However, the whole procedure is not fully consistent, because seasonal adjustment and trend-cycle estimation do not share the same methodological framework, a fact which could potentially entail spurious interpretations. We study this topic from an unified perspective through an extension of Beveridge Nelson decompositions. We show that estimation of the various components of a given time series is feasible once the location of unit roots which drive the persistence of the series have been determined. The precise identification of seasonal unit roots is performed in a preliminary step. Then we derive estimates for each component from a modelization of the raw series which may be parametric (ARMA) or semi parametric, with special attention paid to deterministic components which play a prominent role in the decomposition. Thus, we avoid explicit modelization of each component as required by signal extraction methods or unobserved components analysis. The cycle is simply defined as the stationary stochastic residual of the decomposition. Further properties of this decomposition are investigated in the last part of the paper.Beveridge Nelson decomposition ; Seasonal unit roots ; Seasonal adjustment ; Cycle.