On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with $\gamma=0$. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as $s\to 1$. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with $\beta=0$.Comment: 38 pages, 5 figure

Form factors of twist fields in the lattice Dirac theory

We study U(1) twist fields in a two-dimensional lattice theory of massive Dirac fermions. Factorized formulas for finite-lattice form factors of these fields are derived using elliptic parametrization of the spectral curve of the model, elliptic determinant identities and theta functional interpolation. We also investigate the thermodynamic and the infinite-volume scaling limit, where the corresponding expressions reduce to form factors of the exponential fields of the sine-Gordon model at the free-fermion point.Comment: 20 pages, 2 figure

Entanglement in permutation symmetric states, fractal dimensions, and geometric quantum mechanics

We study the von Neumann and Rényi bipartite entanglement entropies in the thermodynamic limit of many-body quantum states with spin-s sites that possess full symmetry under exchange of sites. It turns out that there is essentially a one-to-one correspondence between such thermodynamic states and probability measures on CP2s. Let a measure be supported on a set of possibly fractal real dimension d with respect to the Study–Fubini metric of CP2s. Let m be the number of sites in a subsystem of the bipartition. We give evidence that in the limit m → ∞, the entanglement entropy diverges like (d/2)logm. Further, if the measure is supported on a submanifold of CP2s and can be described by a density f with respect to the metric induced by the Study–Fubini metric, we give evidence that the correction term is simply related to the entropy associated with f: the geometric entropy of geometric quantum mechanics. This extends results obtained by the authors in a recent letter where the spin-$\frac{1}{2}$ case was considered. Here we provide more examples as well as detailed accounts of the ideas and computations leading to these general results. For special choices of the state in the spin-s situation, we recover the scaling behaviour previously observed by Popkov et al, showing that their result is but a special case of a more general scaling law

Tricritical point of J1-J2 Ising model on hyperbolic lattice

A ferromagnetic-paramagnetic phase transition of the two-dimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains ferromagnetic nearest-neighbor interaction J_1 and the competing antiferromagnetic interaction J_2. A mean-field like second-order phase transition is observed when the ratio \kappa = J_2 / J_1 is less than 0.203. In the region 0.203 < \kappa < 1/4, the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be mean-field like.Comment: 7 pages, 13 figures, submitted to Phys. Rev.

Direct Imaging of Multiple Planets Orbiting the Star HR 8799

Direct imaging of exoplanetary systems is a powerful technique that can reveal Jupiter-like planets in wide orbits, can enable detailed characterization of planetary atmospheres, and is a key step towards imaging Earth-like planets. Imaging detections are challenging due to the combined effect of small angular separation and large luminosity contrast between a planet and its host star. High-contrast observations with the Keck and Gemini telescopes have revealed three planets orbiting the star HR 8799, with projected separations of 24, 38, and 68 astronomical units. Multi-epoch data show counter-clockwise orbital motion for all three imaged planets. The low luminosity of the companions and the estimated age of the system imply planetary masses between 5 and 13 times that of Jupiter. This system resembles a scaled-up version of the outer portion of our Solar System.Comment: 30 pages, 5 figures, Research Article published online in Science Express Nov 13th, 200

Angular Differential Imaging: a Powerful High-Contrast Imaging Technique

Angular differential imaging is a high-contrast imaging technique that reduces quasi-static speckle noise and facilitates the detection of nearby companions. A sequence of images is acquired with an altitude/azimuth telescope while the instrument field derotator is switched off. This keeps the instrument and telescope optics aligned and allows the field of view to rotate with respect to the instrument. For each image, a reference PSF is constructed from other appropriately-selected images of the same sequence and subtracted to remove quasi-static PSF structure. All residual images are then rotated to align the field and are combined. Observed performances are reported for Gemini North data. It is shown that quasi-static PSF noise can be reduced by a factor \~5 for each image subtraction. The combination of all residuals then provides an additional gain of the order of the square root of the total number of acquired images. A total speckle noise attenuation of 20-50 is obtained for one-hour long observing sequences compared to a single 30s exposure. A PSF noise attenuation of 100 was achieved for two-hour long sequences of images of Vega, reaching a 5-sigma contrast of 20 magnitudes for separations greater than 8". For a 30-minute long sequence, ADI achieves 30 times better signal-to-noise than a classical observation technique. The ADI technique can be used with currently available instruments to search for ~1MJup exoplanets with orbits of radii between 50 and 300 AU around nearby young stars. The possibility of combining the technique with other high-contrast imaging methods is briefly discussed.Comment: 27 pages, 7 figures, accepted for publication in Ap

Molecular Hydrogen Kinematics in Cepheus A

We present the radial velocity structure of the molecular hydrogen outflows associated to the star forming region Cepheus A. This structure is derived from doppler shift of the H_2 v=1-0 S(1) emission line obtained by Fabry-Perot spectroscopy. The East and West regions of emission, called Cep A(E) and Cep A(W), show radial velocities in the range -20 to 0 km/s with respect to the molecular cloud. Cep A(W) shows an increasing velocity with position offset from the core indicating the existence of a possible accelarating machanism. Cep A(E) has an almost constant mean radial velocity of -18 km/s along the region although with a large dispersion in velocity, indicating the possibility of a turbulent outflow. A detailed analysis of the Cep A(E) region shows evidence for the presence of a Mach disk on that outflow. Also, we argue that the presence of a velocity gradient in Cep A(W) is indicative of a C-shock in this region. Following Riera et al. (2003), we analyzed the data using wavelet analysis to study the line width and the central radial velocity distributions. We found that both outflows have complex spatial and velocity structures characteristic of a turbulent flow.Comment: 24 pages, 15 figure

Discovery of a Wide Substellar Companion to a Nearby Low-Mass Star

We report the discovery of a wide (135+/-25 AU), unusually blue L5 companion 2MASS J17114559+4028578 to the nearby M4.5 dwarf G 203-50 as a result of a targeted search for common proper motion pairs in the Sloan Digital Sky Survey and the Two Micron All Sky Survey. Adaptive Optics imaging with Subaru indicates that neither component is a nearly equal mass binary with separation > 0.18", and places limits on the existence of additional faint companions. An examination of TiO and CaH features in the primary's spectrum is consistent with solar metallicity and provides no evidence that G 203-50 is metal poor. We estimate an age for the primary of 1-5 Gyr based on activity. Assuming coevality of the companion, its age, gravity and metallicity can be constrained from properties of the primary, making it a suitable benchmark object for the calibration of evolutionary models and for determining the atmospheric properties of peculiar blue L dwarfs. The low total mass (M_tot=0.21+/-0.03 M_sun), intermediate mass ratio (q=0.45+/-0.14), and wide separation of this system demonstrate that the star formation process is capable of forming wide, weakly bound binary systems with low mass and BD components. Based on the sensitivity of our search we find that no more than 2.2% of early-to-mid M dwarfs (9.0 0.06 M_sun.Comment: 24 pages, 5 figures, accepted for publication in Ap

Phase transition of clock models on hyperbolic lattice studied by corner transfer matrix renormalization group method

Two-dimensional ferromagnetic N-state clock models are studied on a hyperbolic lattice represented by tessellation of pentagons. The lattice lies on the hyperbolic plane with a constant negative scalar curvature. We observe the spontaneous magnetization, the internal energy, and the specific heat at the center of sufficiently large systems, where the fixed boundary conditions are imposed, for the cases N>=3 up to N=30. The model with N=3, which is equivalent to the 3-state Potts model on the hyperbolic lattice, exhibits the first order phase transition. A mean-field like phase transition of the second order is observed for the cases N>=4. When N>=5 we observe the Schottky type specific heat below the transition temperature, where its peak hight at low temperatures scales as N^{-2}. From these facts we conclude that the phase transition of classical XY-model deep inside the hyperbolic lattices is not of the Berezinskii-Kosterlitz-Thouless type.Comment: REVTeX style, 4 pages, 6 figures, submitted to Phys. Rev.

Confidence Level and Sensitivity Limits in High Contrast Imaging

In long adaptive optics corrected exposures, exoplanet detections are currently limited by speckle noise originating from the telescope and instrument optics, and it is expected that such noise will also limit future high-contrast imaging instruments for both ground and space-based telescopes. Previous theoretical analysis have shown that the time intensity variations of a single speckle follows a modified Rician. It is first demonstrated here that for a circular pupil this temporal intensity distribution also represents the speckle spatial intensity distribution at a fix separation from the point spread function center; this fact is demonstrated using numerical simulations for coronagraphic and non-coronagraphic data. The real statistical distribution of the noise needs to be taken into account explicitly when selecting a detection threshold appropriate for some desired confidence level. In this paper, a technique is described to obtain the pixel intensity distribution of an image and its corresponding confidence level as a function of the detection threshold. Using numerical simulations, it is shown that in the presence of speckles noise, a detection threshold up to three times higher is required to obtain a confidence level equivalent to that at 5sigma for Gaussian noise. The technique is then tested using TRIDENT CFHT and angular differential imaging NIRI Gemini adaptive optics data. It is found that the angular differential imaging technique produces quasi-Gaussian residuals, a remarkable result compared to classical adaptive optic imaging. A power-law is finally derived to predict the 1-3*10^-7 confidence level detection threshold when averaging a partially correlated non-Gaussian noise.Comment: 29 pages, 13 figures, accepted to Ap