Interference stabilization of autoionizing states in molecular N2N_2 studied by time- and angular-resolved photoelectron spectroscopy

An autoionizing resonance in molecular N$_2$ is excited by an ultrashort XUV pulse and probed by a subsequent weak IR pulse, which ionizes the contributing Rydberg states. Time- and angular-resolved photoelectron spectra recorded with a velocity map imaging spectrometer reveal two electronic contributions with different angular distributions. One of them has an exponential decay rate of $20\pm5$ fs, while the other one is shorter than 10 fs. This observation is interpreted as a manifestation of interference stabilization involving the two overlapping discrete Rydberg states. A formalism of interference stabilization for molecular ionization is developed and applied to describe the autoionizing resonance. The results of calculations reveal, that the effect of the interference stabilization is facilitated by rotationally-induced couplings of electronic states with different symmetry.Comment: 8 pages, 6 figure

"Magic" numbers in Smale's 7th problem

Smale's 7-th problem concerns N-point configurations on the 2-dim sphere which minimize the logarithmic pair-energy V_0(r) = -ln r averaged over the pairs in a configuration; here, r is the chordal distance between the points forming a pair. More generally, V_0(r) may be replaced by the standardized Riesz pair-energy V_s(r)= (r^{-s} -1)/s, which becomes - ln r in the limit s to 0, and the sphere may be replaced by other compact manifolds. This paper inquires into the concavity of the map from the integers N>1 into the minimal average standardized Riesz pair-energies v_s(N) of the N-point configurations on the 2-sphere for various real s. It is known that v_s(N) is strictly increasing for each real s, and for s<2 also bounded above, hence "overall concave." It is (easily) proved that v_{-2}(N) is even locally strictly concave, and that so is v_s(2n) for s<-2. By analyzing computer-experimental data of putatively minimal average Riesz pair-energies v_s^x(N) for s in {-1,0,1,2,3} and N in {2,...,200}, it is found that {v}_{-1}^x(N) is locally strictly concave, while v_s^x(N) is not always locally strictly concave for s in {0,1,2,3}: concavity defects occur whenever N in C^{x}_+(s) (an s-specific empirical set of integers). It is found that the empirical map C^{x}_+(s), with s in {-2,-1,0,1,2,3}, is set-theoretically increasing; moreover, the percentage of odd numbers in C^{x}_+(s), s in {0,1,2,3}, is found to increase with s. The integers in C^{x}_+(0) are few and far between, forming a curious sequence of numbers, reminiscent of the "magic numbers" in nuclear physics. It is conjectured that the "magic numbers" in Smale's 7-th problem are associated with optimally symmetric optimal-energy configurations.Comment: 109 pages, of which 30 are numerical data tables. Thoroughly revised version, to appear in J. Stat. Phys. under the different title: `Optimal N point configurations on the sphere: "Magic" numbers and Smale's 7th problem

Supersolid phase with cold polar molecules on a triangular lattice

We study a system of heteronuclear molecules on a triangular lattice and analyze the potential of this system for the experimental realization of a supersolid phase. The ground state phase diagram contains superfluid, solid and supersolid phases. At finite temperatures and strong interactions there is an additional emulsion region, in contrast to similar models with short-range interactions. We derive the maximal critical temperature $T_c$ and the corresponding entropy $S/N = 0.04(1)$ for supersolidity and find feasible experimental conditions for its realization.Comment: 4 pages, 4 figure

Effects of mavoglurant on visual attention and pupil reactivity while viewing photographs of faces in Fragile X Syndrome.

BackgroundNumerous preclinical studies have supported the theory that enhanced activation of mGluR5 signaling, due to the absence or reduction of the FMR1 protein, contributes to cognitive and behavioral deficits in patients with fragile X syndrome (FXS). However multiple phase 2 controlled trials in patients with FXS have failed to demonstrate efficacy of compounds that negatively modulate mGluR5, including two phase 2b randomized controlled trials (RCT) of mavoglurant (AFQ056, Novartis Pharma AG), when the primary measures of interest were behavioral ratings. This has cast some doubt onto the translation of the mGluR5 theory from animal models to humans with the disorder.MethodsWe evaluated social gaze behavior-a key phenotypic feature of the disorder-and sympathetic nervous system influence on pupil size using a previously-validated eye tracking paradigm as a biobehavioral probe, in 57 adolescent or adult patients with FXS at baseline and following three months of blinded treatment with one of three doses of mavoglurant or placebo, within the context of the AFQ056 RCTs.ResultsPatients with FXS treated with mavoglurant demonstrated increased total absolute looking time and number of fixations to the eye region while viewing human faces relative to baseline, and compared to those treated with placebo. In addition, patients had greater pupil reactivity to faces relative to baseline following mavoglurant treatment compared to placebo.DiscussionThe study shows that negative modulation of mGluR5 activity improves eye gaze behavior and alters sympathetically-driven reactivity to faces in patients with FXS, providing preliminary evidence of this drug's impact on behavior in humans with the disorder

Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

Quasi-Lie schemes and Emden--Fowler equations

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from this new perspective. Finally some t-dependent constants of the motion for equations of Emden type satisfying certain conditions are recovered

Christmas Island lagoonal lakes, models for the deposition of carbonate–evaporite–organic laminated sediments

The atoll of Christmas Island (now known as Kiritimati) in the Kiribati Republic (Central Pacific) lies at about 2°N in the intertropical convergence zone. Much of the surface area of the atoll (ca. 360 km2) is occupied by numerous lakes in which carbonate, evaporite (calcium sulfate, halite) and organic layers are deposited. Observations suggest that deposition of these different laminae is controlled by climatic and biologic factors. It is thought that periodic climatic variations, such as El Niño-Southern Oscillations (ENSO) events which bring heavy rainfall to the atoll, result in the succession of the precipitation of carbonate minerals (during periods after dilution of hypersaline waters by heavy rains), followed by evaporitic minerals (carbonate, calcium sulfate, halite) when salinity increases through evaporation. Thick (up to 5 cm) microbial (essentially cyanobacterial) mats develop continuously on the lake bottom surfaces providing the sediment with an important (total organic carbon 2–5%) organic contribution in the form of an internal, geometrically structured, network in which the authigenic minerals precipitate. The high bioproductivity of these microbial populations is reflected in low δ13C values of sedimentary organic carbon (−14 to −17‰), interpreted as being the result of high atmospheric CO2 demand (Geochim. Cosmochim. Acta, 56 (1992) 335). The well-laminated organic layers present in the sediment profile result from the death and burial of microbial populations at the time of severe climatic events (storms, heavy rainfall). These lagoonal lakes provide a model for the deposition of carbonate and organic matter in an evaporitic environment. The high ratio of deposited carbonate vs. sulfate+chloride, when compared to low ratio in evaporitic salinas, results from both a lack of limitation of calcium, magnesium and carbonate ions (in a carbonate reef environment) and active processes of high-Mg calcite precipitation (organomineralization)

Big rip avoidance via black holes production

We consider a cosmological scenario in which the expansion of the Universe is dominated by phantom dark energy and black holes which condense out of the latter component. The mass of black holes decreases via Hawking evaporation and by accretion of phantom fluid but new black holes arise continuously whence the overall evolution can be rather complex. We study the corresponding dynamical system to unravel this evolution and single out scenarios where the big rip singularity does not occur.Comment: 16 pages, two figures. Key words. Cosmology, phantom energy, black holes. Sligthly extended version to be published in Gravitation and Cosmolog