Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

HST hot-Jupiter transmission spectral survey: Haze in the atmosphere of WASP-6b

We report Hubble Space Telescope (HST) optical to near-infrared transmission spectroscopy of the hot Jupiter WASP-6b, measured with the Space Telescope Imaging Spectrograph (STIS) and Spitzer's InfraRed Array Camera (IRAC). The resulting spectrum covers the range $0.29-4.5\,\mu$m. We find evidence for modest stellar activity of WASP-6b and take it into account in the transmission spectrum. The overall main characteristic of the spectrum is an increasing radius as a function of decreasing wavelength corresponding to a change of $\Delta (R_p/R_{\ast})=0.0071$ from 0.33 to $4.5\,\mu$m. The spectrum suggests an effective extinction cross-section with a power law of index consistent with Rayleigh scattering, with temperatures of $973\pm144$ K at the planetary terminator. We compare the transmission spectrum with hot-Jupiter atmospheric models including condensate-free and aerosol-dominated models incorporating Mie theory. While none of the clear-atmosphere models is found to be in good agreement with the data, we find that the complete spectrum can be described by models that include significant opacity from aerosols including Fe-poor Mg$_2$SiO$_4$, MgSiO$_3$, KCl and Na$_2$S dust condensates. WASP-6b is the second planet after HD189733b which has equilibrium temperatures near $\sim1200$ K and shows prominent atmospheric scattering in the optical.Comment: 18 pages, 15 figures, 7 table

Fermionic coherent states for pseudo-Hermitian two-level systems

We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to such systems. Pseudo-fermionic coherent states are constructed as eigenstates of two pseudo-fermion annihilation operators. These coherent states form a bi-normal and bi-overcomplete system, and their evolution governed by the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the introduced pseudo-fermion operators the two-level system' Hamiltonian takes a factorized form similar to that of a harmonic oscillator.Comment: 13 pages (Latex, article class), no figures; v2: some amendments in section 2, seven new refs adde

HST hot Jupiter transmission spectral survey: evidence for aerosols and lack of TiO in the atmosphere of WASP-12b

We present HST optical transmission spectra of the transiting hot Jupiter WASP-12b, taken with the STIS instrument. From the transmission spectra, we are able to decisively rule out prominent absorption by TiO in the exoplanet's atmosphere. Strong pressure-broadened Na and K absorption signatures are also excluded, as are significant metal-hydride features. We compare our combined broadband spectrum to a wide variety of existing aerosol-free atmospheric models, though none are satisfactory fits. However, we do find that the full transmission spectrum can be described by models which include significant opacity from aerosols: including Rayleigh scattering, Mie scattering, tholin haze, and settling dust profiles. The transmission spectrum follows an effective extinction cross section with a power-law of index alpha, with the slope of the transmission spectrum constraining the quantity alphaT = -3528+/-660 K, where T is the atmospheric temperature. Rayleigh scattering (alpha=-4) is among the best fitting models, though requires low terminator temperatures near 900 K. Sub-micron size aerosol particles can provide equally good fits to the entire transmission spectrum for a wide range of temperatures, and we explore corundum as a plausible dust aerosol. The presence of atmospheric aerosols also helps to explain the modestly bright albedo implied by Spitzer observations, as well as the near black body nature of the emission spectrum. Ti-bearing condensates on the cooler night-side is the most natural explanation for the overall lack of TiO signatures in WASP-12b, indicating the day/night cold-trap is an important effect for very hot Jupiters. These finding indicate that aerosols can play a significant atmospheric role for the entire wide range of hot-Jupiter atmospheres, potentially affecting their overall spectrum and energy balance.(abridged)Comment: 19 pages, 14 figures, 5 tables. Accepted for publication in MNRA

Bose-Einstein condensation in trapped dipolar gases

We discuss Bose-Einstein condensation in a trapped gas of bosonic particles interacting dominantly via dipole-dipole forces. We find that in this case the mean-field interparticle interaction and, hence, the stability diagram are governed by the trapping geometry. Possible physical realisations include ultracold heteronuclear molecules, or atoms with laser induced electric dipole moments.Comment: 4 pages, 4 figure

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.Comment: Review article, will be published in Journal of Optics B, special issue on Optical Solitons, 6 figure

Surface Symmetry Energy of Nuclear Energy Density Functionals

We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron- rich matter and description of fission rates for r-process nucleosynthesis.Comment: 16 pages, submitted to Phys. Rev.

GTC OSIRIS transiting exoplanet atmospheric survey: detection of potassium in HAT-P-1b from narrow-band spectrophotometry

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2015 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.We present the detection of potassium in the atmosphere of HAT-P-1b using optical transit narrow-band photometry. The results are obtained using the 10.4-m Gran Telescopio Canarias together with the OSIRIS instrument in tunable filter imaging mode. We observed four transits, two at continuum wavelengths outside the potassium feature, at 6792 and 8844 Å, and two probing the potassium feature in the line wing at 7582.0 Å and the line core at 7664.9 Å using a 12 Å filter width (R ∼ 650). The planet-to-star radius ratios in the continuum are found to be Rpl/R⋆ = 0.1176 ± 0.0013 at 6792 Å and Rpl/R⋆ = 0.1168 ± 0.0022 at 8844 Å, significantly lower than the two observations in the potassium line: Rpl/R⋆ = 0.1248 ± 0.0014 in the line wing at 7582.0 Å and Rpl/R⋆ = 0.1268 ± 0.0012 in the line core at 7664.9 Å. With a weighted mean of the observations outside the potassium feature Rpl/R⋆ = 0.1174 ± 0.0010, the potassium is detected as an increase in the radius ratio of Delta Rpl/R⋆ = 0.0073 ± 0.0017 at 7582.0 Å and Delta Rpl/R⋆ = 0.0094 ± 0.0016 at 7664.9 Å (a significance of 4.3σ and 6.1σ, respectively). We hypothesize that the strong detection of potassium is caused by a large scaleheight, which can be explained by a high temperature at the base of the upper atmosphere. A lower mean molecular mass caused by the dissociation of molecular hydrogen into atomic hydrogen by the extreme ultraviolet flux from the host star may also partly explain the amplitude of our detection.European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)Science & Technology Facilities Council (STFC)Space Telescope Science InstituteHalliday fellowshipFrench Agence Nationale de la Recherche (ANR), under programme ANR-12-BS05-0012 ‘Exo-Atmos