Linear polarization scans for resonant X‐ray diffraction with a double‐phase‐plate configuration

An in‐vacuum double‐phase‐plate diffractometer for performing polarization scans combined with resonant X‐ray diffraction experiments is presented. The use of two phase plates enables the correction of some of the aberration effects owing to the divergence of the beam and its energy spread. A higher rate of rotated polarization is thus obtained in comparison with a system with only a single retarder. Consequently, thinner phase plates can be used to obtain the required rotated polarization rate. These results are particularly interesting for applications at low energy (e.g. 4 keV) where the absorption owing to the phase plate(s) plays a key role in the feasibility of these experiments. Measurements by means of polarization scans at the uranium M₄ edge on UO₂ enable the contributions of the magnetic and quadrupole ordering in the material to be disentangled.     

Random quantum operations

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Φ associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of Φ and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.     

Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help.     

Metal-ligand solution equilibria studied by electrospray ionization mass spectrometry: effect of instrumental parameters

Electrospray ionization mass spectrometry (ESI-MS) is being increasingly employed in the study of metal-ligand equilibria in aqueous solution. In the present work, the ESI-MS spectral changes due to different settings of the following instrumental parameters are analyzed: the solution flow rate (F(S)), the nebulizer gas flow rate (F(G)), the sprayer potential (E), and the temperature of the entrance capillary (T). Twenty-eight spectra were obtained for each of six samples containing aluminum(III) and 2,3-dihydroxypyridine at various pH, in the absence or in the presence of a buffer and of sodium ions. Among the considered instrumental parameters, T produced the largest effects on the ionic intensities. F(S) and F(G) affected the ESI-MS spectra to a lower extent than T. In the investigated conditions E had the weakest effects on the spectra.The correlations observed between the ionic intensities and these instrumental parameters were interpreted considering the presence of three kinds of perturbations occurring in the ESI-MS ion source: formation of some dimers in the droplets, different transfer efficiencies from the droplets to the gas phase for different complexes (according to their surface activity), and subsequent partial thermal decomposition of the dimers and of one of the monomeric complexes in the gas phase. Our results show that the evaluation of the effects produced in the ESI-MS spectra by a change of instrumental parameters can allow to identify the perturbations occurring when metal-ligand solutions are studied by ESI-MS.     

Gravitational lensing by black holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.     

Pulsation of black holes

The Hawking–Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner–Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum “beating heart” are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.     

Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns

Journal of Statistical Physics - The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a...     

Equivalence of Non-equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model

We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive \(N\) -degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. For each value of the forcing, the statistical properties of the irreversible and reversible model are in excellent agreement, if in the latter the energy is kept constant at a value equal to the time-average realized with the irreversible model. In particular, the average contraction rate of the phase space of the time-reversible model agrees with that of the irreversible model, where instead it is constant by construction. We also show that the phase space contraction rate obeys the fluctuation relation, and we relate its finite time corrections to the characteristic time scales of the system. A local version of the fluctuation relation is explored and successfully checked. The equivalence between the two non-equilibrium ensembles extends to dynamical properties such as the Lyapunov exponents, which are shown to obey to a good degree of approximation a pairing rule. These results have relevance in motivating the importance of the chaotic hypothesis. in explaining that we have the freedom to model non-equilibrium systems using different but equivalent approaches, and, in particular, that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.     

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

In this paper we provide a connection between the geometrical properties of the attractor of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan–Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.     

X‐ray‐excited optical luminescence and X‐ray absorption fine‐structures studies of CdWO4 scintillator

X‐ray‐excited optical luminescence (XEOL) emission and excitation spectra as well as the EXAFS signal of CdWO₄ were measured in the energy region of the Cd and W absorption edges. From EXAFS refinement, structural parameters such as number of atoms, distance from the absorbing atom and width of coordination shells in the W neighborhood were determined. The role of W–O interactions on the intrinsic luminescence of CdWO₄ is discussed. The efficiencies of conversion, transfer and emission processes involved in the scintillation mechanism showed to be high when self‐trapped excitons are formed locally by direct excitation of W ions. Annihilation of these excitons provides the characteristic scintillation of CdWO₄, a broad band emission with maximum at 500 nm. The presence of two energetically different O positions in the lattice gives rise to the composite structure of the luminescence band, and no influence of extrinsic defects was noticed. A mismatch between the X‐ray absorption coefficient and the zero‐order luminescence curves corroborates that the direct excitation of Cd ions induces secondary electronic excitations not very effective in transferring energy to the luminescent group, WO₆.