The Conformal Window of deformed CFT's in the planar limit

We discuss in the planar approximation the effect of double-trace deformations on CFT's. We show that this large class of models posses a conformal window describing a non-trivial flow between two fixed points of the renormalization group, and reveal the presence of a resonance which we associate to the remnant of a dilaton pole. As the conformal window shrinks to zero measure the theory undergoes a conformal phase transition separating a symmetric from a nonsymmetric phase. The recently conjectured strongly coupled branch of non-supersymmetric, non-abelian gauge theories with a large number of flavors is analyzed in light of these results, and a model for the strong branch is proposed. Some phenomenological implications in the context of unparticle physics are also emphasized.Comment: 15 pages PRD class, 2 figures, to be published in PR

Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets

We investigate the interplay between frustration and zero-point quantum fluctuations in the ground state of the triangular and $J_1{-}J_2$ Heisenberg antiferromagnets, using finite-size spin-wave theory, exact diagonalization, and quantum Monte Carlo methods. In the triangular Heisenberg antiferromagnet, by performing a systematic size-scaling analysis, we have obtained strong evidences for a gapless spectrum and a finite value of the thermodynamic order parameter, thus confirming the existence of long-range N\'eel order.The good agreement between the finite-size spin-wave results and the exact and quantum Monte Carlo data also supports the reliability of the spin-wave expansion to describe both the ground state and the low-energy spin excitations of the triangular Heisenberg antiferromagnet. In the $J_1{-}J_2$ Heisenberg model, our results indicate the opening of a finite gap in the thermodynamic excitation spectrum at $J_2/J_1 \simeq 0.4$, marking the melting of the antiferromagnetic N\'eel order and the onset of a non-magnetic ground state. In order to characterize the nature of the latter quantum-disordered phase we have computed the susceptibilities for the most important crystal symmetry breaking operators. In the ordered phase the effectiveness of the spin-wave theory in reproducing the low-energy excitation spectrum suggests that the uniform spin susceptibility of the model is very close to the linear spin-wave prediction.Comment: Review article, 44 pages, 18 figures. See also PRL 87, 097201 (2001

Titan solar occultation observations reveal transit spectra of a hazy world

High altitude clouds and hazes are integral to understanding exoplanet observations, and are proposed to explain observed featureless transit spectra. However, it is difficult to make inferences from these data because of the need to disentangle effects of gas absorption from haze extinction. Here, we turn to the quintessential hazy world -- Titan -- to clarify how high altitude hazes influence transit spectra. We use solar occultation observations of Titan's atmosphere from the Visual and Infrared Mapping Spectrometer (VIMS) aboard NASA's Cassini spacecraft to generate transit spectra. Data span 0.88-5 microns at a resolution of 12-18 nm, with uncertainties typically smaller than 1%. Our approach exploits symmetry between occultations and transits, producing transit radius spectra that inherently include the effects of haze multiple scattering, refraction, and gas absorption. We use a simple model of haze extinction to explore how Titan's haze affects its transit spectrum. Our spectra show strong methane absorption features, and weaker features due to other gases. Most importantly, the data demonstrate that high altitude hazes can severely limit the atmospheric depths probed by transit spectra, bounding observations to pressures smaller than 0.1-10 mbar, depending on wavelength. Unlike the usual assumption made when modeling and interpreting transit observations of potentially hazy worlds, the slope set by haze in our spectra is not flat, and creates a variation in transit height whose magnitude is comparable to those from the strongest gaseous absorption features. These findings have important consequences for interpreting future exoplanet observations, including those from NASA's James Webb Space Telescope.Comment: Updated journal reference; data available via http://sites.google.com/site/tdrobinsonscience/science/tita

Hardy's proof of nonlocality in the presence of noise

We extend the validity of Hardy's nonlocality without inequalities proof to cover the case of special one-parameter classes of non-pure statistical operators. These mixed states are obtained by mixing the Hardy states with a completely chaotic noise or with a colored noise and they represent a realistic description of imperfect preparation processes of (pure) Hardy states in nonlocality experiments. Within such a framework we are able to exhibit a precise range of values of the parameter measuring the noise affecting the non-optimal preparation of an arbitrary Hardy state, for which it is still possible to put into evidence genuine nonlocal effects. Equivalently, our work exhibits particular classes of bipartite mixed states whose constituents do not admit any local and deterministic hidden variable model reproducing the quantum mechanical predictions.Comment: 9 pages, 2 figures, RevTex, revised versio

Greenberger-Horne-Zeilinger argument of nonlocality without inequalities for mixed states

We generalize the Greenberger-Horne-Zeilinger nonlocality without inequalities argument to cover the case of arbitrary mixed statistical operators associated to three-qubits quantum systems. More precisely, we determine the radius of a ball (in the trace distance topology) surrounding the pure GHZ state and containing arbitrary mixed statistical operators which cannot be described by any local and realistic hidden variable model and which are, as a consequence, noncompletely separable. As a practical application, we focus on certain one-parameter classes of mixed states which are commonly considered in the experimental realization of the original GHZ argument and which result from imperfect preparations of the pure GHZ state. In these cases we determine for which values of the parameter controlling the noise a nonlocality argument can still be exhibited, despite the mixedness of the considered states. Moreover, the effect of the imperfect nature of measurement processes is discussed.Comment: 8 pages, RevTex; added references, corrected typo

Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames

By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of mass (described by frozen Jacobi data) carrying a pole-dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field we obtain both Maxwell equations and their Hamiltonian description in non-inertial frames. Then by means of a non-covariant decomposition we define the non-inertial radiation gauge and we find the form of the non-covariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit. In the second paper we will study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect will be given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.Comment: This paper and the second one are an adaptation of arXiv 0812.3057 for publication on Int.J.Geom. Methods in Modern Phys. 77

Coupled-mode theory for photonic band-gap inhibition of spatial instabilities

We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane