Symmetry characterization of the collective modes of the phase diagram of the ν=0\nu=0 quantum Hall state in graphene: Mean-field and spontaneously broken symmetries

We devote this work to the study of the mean-field phase diagram of the $\nu=0$ quantum Hall state in bilayer graphene and the computation of the corresponding neutral collective modes, extending the results of recent works in the literature. Specifically, we provide a detailed classification of the complete orbital-valley-spin structure of the collective modes and show that phase transitions are characterized by singlet modes in orbital pseudospin, which are independent of the Coulomb strength and suffer strong many-body corrections from short-range interactions at low momentum. We describe the symmetry breaking mechanism for phase transitions in terms of the valley-spin structure of the Goldstone modes. For the remaining phase boundaries, we prove that the associated exact $SO(5)$ symmetry existing at zero Zeeman energy and interlayer voltage survives as a weaker mean-field symmetry of the Hartree-Fock equations. We extend the previous results for bilayer graphene to the monolayer scenario. Finally, we show that taking into account Landau level mixing through screening does not modify the physical picture explained above.Comment: 44 pages, 10 figure

Violation of Cauchy-Schwarz inequalities by spontaneous Hawking radiation in resonant boson structures

The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree of CS violation and the maximum violation temperature for a double barrier structure separating two regions of subsonic and supersonic condensate flow. We also consider the case where the resonant sonic horizon is produced by a space-dependent contact interaction. In some cases, CS violation can be observed by direct atom counting in a time-of-flight experiment. We show that near the conventional zero-frequency radiation peak, the decisive CS violation cannot occur.Comment: 10 pages, 6 figure

Entanglement and violation of classical inequalities in the Hawking radiation of flowing atom condensates

We consider a sonic black-hole scenario where an atom condensate flows through a subsonic-supersonic interface. We discuss several criteria that reveal the existence of nonclassical correlations resulting from the quantum character of the spontaneous Hawking radiation. We unify previous general work as applied to Hawking radiation analogs. We investigate the measurability of the various indicators and conclude that, within a class of detection schemes, only the violation of quadratic Cauchy-Schwarz inequalities can be discerned. We show numerical results that further support the viability of measuring deep quantum correlations in concrete scenarios.Comment: 15 pages, 6 figure

Radial Distribution of Particle Clusters in Down Flow Reactors

Particle clustering is of major importance in down flow reactors having a profound influence on some fundamental properties of the flowing suspension such as particle slip velocity. The goal of this study is to provide further evidence to support the formation of clusters using the novel CREC-GS-Optiprobes. This sensor is equipped with GRIN lenses and introduces minimum intrusion effects. Results reported include radial distributions of particle cluster size and velocity under various gas flow superficial velocities and suspension densities. Micro-scale and macro-scale flow structures are advanced on the basis of the reported data

Long time universality of black-hole lasers

For flowing quantum gases, it has been found that at long times an initial black-hole laser (BHL) configuration exhibits only two possible states: the ground state or a periodic self-oscillating state of continuous emission of solitons. So far, all the works on this subject are based on a highly idealized model, quite difficult to implement experimentally. Here we study the instability spectrum and the time evolution of a recently proposed realistic model of a BHL, thus providing a useful theoretical tool for the clear identification of black-hole lasing in future experiments. We further confirm the existence of a well-defined phase diagram at long times, which bespeaks universality in the long-time behavior of a BHL. Additionally, we develop a complementary model in which the same potential profile is applied to a subsonic homogeneous flowing condensate that, despite not forming a BHL, evolves towards the same phase diagram as the associated BHL model. This result reveals an even stronger form of robustness in the long-time behavior with respect to the transient, which goes beyond what has been described in the previous literature.Comment: 14 pages, 8 figures. Final version of the manuscrip

Theta-13 as a Probe of Mu-Tau symmetry for Leptons

Many experiments are being planned to measure the neutrino mixing parameter $\theta_{13}$ using reactor as well as accelerator neutrino beams. In this note, the theoretical significance of a high precision measurement of this parameter is discussed. It is emphasized that it will provide crucial information about different ways to understand the origin of large atmospheric neutrino mixing and move us closer towards determining the neutrino mass matrix. For instance if exact $\mu\leftrightarrow \tau$ symmetry in the neutrino mass matrix is assumed to be the reason for maximal $\nu_\mu-\nu_\tau$ mixing, one gets $\theta_{13}=0$. Whether $\theta_{13}\simeq \sqrt{\Delta m^2_{\odot}/\Delta m^2_A}$ or $\theta_{13}\simeq \Delta m^2_{\odot}/\Delta m^2_A$ can provide information about the way the $\mu\leftrightarrow \tau$ symmetry breaking manifests in the case of normal hierarchy. We also discuss the same question for inverted hierarchy as well as possible gauge theories with this symmetry.Comment: 12 pages; no figures; latex; more exact expressions given for some parameters and minor typos corrected; paper accepted for publication in JHE

Prediction of Herbage Accumulation of \u3ci\u3eCynodon\u3c/i\u3e Grasses by an Empirical Model Based on Temperature and Daylength

The objective of this work was to estimate dry matter production of Cynodon grasses as a function of photothermal units (PU). Total PU values were calculated for the period from February 1 to April 24, 1996, from a location in southeastern Brazil. Regression analysis was run between PU and herbage production from a published data set on five Cynodon cultivars, with an r2 of 0.9983. Differences between measured and estimated values were under 5%. Model testing using an independent data set on herbage dry matter production from grazed Cynodon pastures showed an overestimation, probably due to water deficit during the experimental period. In addition, grazing intensity may have been a reason for the less than optimal fit. The model was adequate in predicting the variation in production potential throughout the periods studied although modifications to include the effect of water balance, nitrogen fertilization and defoliation intensity may allow for better predictions under sub-optimal environmental conditions and varying management strategies