Stable gauged maps

We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt, and the associated integrals giving rise to gauged Gromov-Witten invariants. We survey various applications to cohomological and K-theoretic Gromov-Witten invariants.Comment: Survey for the 2015 AMS Summer Institute on Algebraic Geometry. Split off from the more technical paper "Properness for scaled gauged maps" [arXiv:1606.01383]. There is still substantial overlap between the two papers. This version has minor correction

Fast-to-Alfv\'en mode conversion mediated by Hall current. II Application to the solar atmosphere

Coupling between fast magneto-acoustic and Alfv\'en waves can be observe in fully ionized plasmas mediated by stratification and 3D geometrical effects. In Paper I, Cally & Khomenko (2015) have shown that in a weakly ionized plasma, such as the solar photosphere and chromosphere, the Hall current introduces a new coupling mechanism. The present study extends the results from Paper I to the case of warm plasma. We report on numerical experiments where mode transformation is studied using quasi-realistic stratification in thermodynamic parameters resembling the solar atmosphere. This redresses the limitation of the cold plasma approximation assumed in Paper I, in particular allowing the complete process of coupling between fast and slow magneto-acoustic modes and subsequent coupling of the fast mode to the Alfv\'en mode through the Hall current. Our results confirm the efficacy of the mechanism proposed in Paper I for the solar case. We observe that the efficiency of the transformation is a sensitive function of the angle between the wave propagation direction and the magnetic field, and of the wave frequency. The efficiency increases when the field direction and the wave direction are aligned for increasing wave frequencies. After scaling our results to typical solar values, the maximum amplitude of the transformed Alfv\'en waves, for a frequency of 1 Hz, corresponds to an energy flux (measured above the height of peak Hall coupling) of $\sim10^3$ $\rm W\,m^{-2}$, based on an amplitude of 500 $\rm m\,s^{-1}$ at $\beta=1$, which is sufficient to play a major role in both quiet and active region coronal heating

Non-Gaussianity analysis on local morphological measures of WMAP data

The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity, and elongation of the signal's local features. In the present work, the non-Gaussianity of the WMAP temperature data of the cosmic microwave background (CMB) is analyzed in terms of the first four moments of the statistically isotropic random fields associated with these local morphological measures, at wavelet scales corresponding to angular sizes between 27.5 arcminutes and 30 degrees on the celestial sphere. While no detection is made neither in the orientation analysis nor in the elongation analysis, a strong detection is made in the excess kurtosis of the signed-intensity of the WMAP data. The non-Gaussianity is observed with a significance level below 0.5% at a wavelet scale corresponding to an angular size around 10 degrees, and confirmed at neighbour scales. This supports a previous detection of an excess of kurtosis in the wavelet coefficient of the WMAP data with the axisymmetric Mexican hat wavelet (Vielva et al. 2004). Instrumental noise and foreground emissions are not likely to be at the origin of the excess of kurtosis. Large-scale modulations of the CMB related to some unknown systematics are rejected as possible origins of the detection. The observed non-Gaussianity may therefore probably be imputed to the CMB itself, thereby questioning the basic inflationary scenario upon which the present concordance cosmological model relies. Taking the CMB temperature angular power spectrum of the concordance cosmological model at face value, further analysis also suggests that this non-Gaussianity is not confined to the directions on the celestial sphere with an anomalous signed-intensity.Comment: 10 pages, 3 figures. Version 2 includes minor changes to match version accepted for publication in MNRA

An explanation of the Δ5/2−(1930)\Delta_{5/2^{-}}(1930) as a ρΔ\rho\Delta bound state

We use the $\rho\Delta$ interaction in the hidden gauge formalism to dynamically generate $N^{\ast}$ and $\Delta^{\ast}$ resonances. We show, through a comparison of the results from this analysis and from a quark model study with data, that the $\Delta_{5/2^{-}}(1930),$ $\Delta_{3/2^{-}}(1940)$ and $\Delta_{1/2^{-}}(1900)$ resonances can be assigned to $\rho\Delta$ bound states. More precisely the $\Delta_{5/2^{-}}(1930)$ can be interpreted as a $\rho\Delta$ bound state whereas the $\Delta_{3/2^{-}}(1940)$ and $\Delta_{1/2^{-}}(1900)$ may contain an important $\rho\Delta$ component. This interpretation allows for a solution of a long-standing puzzle concerning the description of these resonances in constituent quark models. In addition we also obtain degenerate $J^{P}=1/2^{-},3/2^{-},5/2^{-}$ $N^{*}$ states but their assignment to experimental resonances is more uncertain.Comment: 19 pags, 8 fig

Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensions vanish when the number of coupled chains goes to infinity, implying the Fermi liquid behavior of a 2D system in that limit. However, when the Fermi level is at the Van Hove singularity arising from the saddle points of the 2D dispersion, backscattering and Cooper-pair scattering lead to the breakdown of the metallic behavior at low energies. These interactions are taken into account through their renormalization group scaling, studying in turn their influence on the nonperturbative bosonization of the model. We show that, at a certain low-energy scale, the anomalous electron dimension diverges at the Fermi points closer to the saddle points of the 2D dispersion. The d-wave superconducting correlations become also large at low energies, but their growth is cut off as the suppression of fermion excitations takes place first, extending progressively along the Fermi points towards the diagonals of the 2D Brillouin zone. We stress that this effect arises from the vanishing of the charge stiffness at the Fermi points, characterizing a critical behavior that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure

Plausible explanation of the Δ5/2+(2000)\Delta_{5/2^{+}}(2000) puzzle

From a Faddeev calculation for the $\pi-(\Delta\rho)_{N_{5/2^{-}}(1675)}$ system we show the plausible existence of three dynamically generated $I(J^{P})=3/2 (5/2^{+})$ baryon states below 2.3 GeV whereas only two resonances, $\Delta_{5/2^{+}}(1905)(\ast\ast\ast\ast)$ and $\Delta_{5/2^{+}}(2000)(\ast\ast),$ are cataloged in the Particle Data Book Review. Our results give theoretical support to data analyses extracting two distinctive resonances, $\Delta_{5/2^{+}}(\sim1740)$ and $\Delta_{5/2^{+}}(\sim2200),$ from which the mass of $\Delta_{5/2^{+}}(2000)(\ast\ast)$ is estimated. We propose that these two resonances should be cataloged instead of $\Delta_{5/2^{+}}(2000).$ This proposal gets further support from the possible assignment of the other baryon states found in the approach in the $I=1/2,3/2$ with $J^{P}=1/2^{+},3/2^{+},5/2^+$ sectors to known baryonic resonances. In particular, $\Delta_{1/2^{+}}(1750)(\ast)$ is naturally interpreted as a $\pi N_{1/2^{-}}(1650)$ bound state.Comment: 13 pages, 7 figure

On the void explanation of the Cold Spot

The integrated Sachs-Wolfe (ISW) contribution induced on the cosmic microwave background by the presence of a supervoid as the one detected by Szapudi et al. (2015) is reviewed in this letter in order to check whether it could explain the Cold Spot (CS) anomaly. Two different models, previously used for the same purpose, are considered to describe the matter density profile of the void: a top hat function and a compensated profile produced by a Gaussian potential. The analysis shows that, even enabling ellipticity changes or different values for the dark-energy equation of state parameter $\omega$, the ISW contribution due to the presence of the void does not reproduce the properties of the CS. Finally, the probability of alignment between the void and the CS is also questioned as an argument in favor of a physical connection between these two phenomena

Tunable entanglement distillation of spatially correlated down-converted photons

We report on a new technique for entanglement distillation of the bipartite continuous variable state of spatially correlated photons generated in the spontaneous parametric down-conversion process (SPDC), where tunable non-Gaussian operations are implemented and the post-processed entanglement is certified in real-time using a single-photon sensitive electron multiplying CCD (EMCCD) camera. The local operations are performed using non-Gaussian filters modulated into a programmable spatial light modulator and, by using the EMCCD camera for actively recording the probability distributions of the twin-photons, one has fine control of the Schmidt number of the distilled state. We show that even simple non-Gaussian filters can be finely tuned to a ~67% net gain of the initial entanglement generated in the SPDC process.Comment: 12 pages, 6 figure