Exact Integration of the High Energy Scale in Doped Mott Insulators

We expand on our earlier work (cond-mat/0612130, Phys. Rev. Lett. {\bf 99}, 46404 (2007)) in which we constructed the exact low-energy theory of a doped Mott insulator by explicitly integrating (rather than projecting) out the degrees of freedom far away from the chemical potential. The exact low-energy theory contains degrees of freedom that cannot be obtained from projective schemes. In particular a new charge $\pm 2e$ bosonic field emerges at low energies that is not made out of elemental excitations. Such a field accounts for dynamical spectral weight transfer across the Mott gap. At half-filling, we show that two such excitations emerge which play a crucial role in preserving the Luttinger surface along which the single-particle Green function vanishes. In addition, the interactions with the bosonic fields defeat the artificial local SU(2) symmetry that is present in the Heisenberg model. We also apply this method to the Anderson-U impurity and show that in addition to the Kondo interaction, bosonic degrees of freedom appear as well. Finally, we show that as a result of the bosonic degree of freedom, the electron at low energies is in a linear superposition of two excitations--one arising from the standard projection into the low-energy sector and the other from the binding of a hole and the boson.Comment: Published veriso

Constraining the Atmospheric Composition of the Day-Night Terminators of HD 189733b : Atmospheric Retrieval with Aerosols

A number of observations have shown that Rayleigh scattering by aerosols dominates the transmission spectrum of HD 189733b at wavelengths shortward of 1 $\mu$m. In this study, we retrieve a range of aerosol distributions consistent with transmission spectroscopy between 0.3-24 $\mu$m that were recently re-analyzed by Pont et al. (2013). To constrain the particle size and the optical depth of the aerosol layer, we investigate the degeneracies between aerosol composition, temperature, planetary radius, and molecular abundances that prevent unique solutions for transit spectroscopy. Assuming that the aerosol is composed of MgSiO$_3$, we suggest that a vertically uniform aerosol layer over all pressures with a monodisperse particle size smaller than about 0.1 $\mu$m and an optical depth in the range 0.002-0.02 at 1 $\mu$m provides statistically meaningful solutions for the day/night terminator regions of HD 189733b. Generally, we find that a uniform aerosol layer provide adequate fits to the data if the optical depth is less than 0.1 and the particle size is smaller than 0.1 $\mu$m, irrespective of the atmospheric temperature, planetary radius, aerosol composition, and gaseous molecules. Strong constraints on the aerosol properties are provided by spectra at wavelengths shortward of 1 $\mu$m as well as longward of 8 $\mu$m, if the aerosol material has absorption features in this region. We show that these are the optimal wavelengths for quantifying the effects of aerosols, which may guide the design of future space observations. The present investigation indicates that the current data offer sufficient information to constrain some of the aerosol properties of HD189733b, but the chemistry in the terminator regions remains uncertain.Comment: Transferred to ApJ and accepted. 11 pages, 10 figures, 1 tabl

Seasonal Variability of Saturn's Tropospheric Temperatures, Winds and Para-H2_2 from Cassini Far-IR Spectroscopy

Far-IR 16-1000 $\mu$m spectra of Saturn's hydrogen-helium continuum measured by Cassini's Composite Infrared Spectrometer (CIRS) are inverted to construct a near-continuous record of upper tropospheric (70-700 mbar) temperatures and para-H$_2$ fraction as a function of latitude, pressure and time for a third of a Saturnian year (2004-2014, from northern winter to northern spring). The thermal field reveals evidence of reversing summertime asymmetries superimposed onto the belt/zone structure. The temperature structure that is almost symmetric about the equator by 2014, with seasonal lag times that increase with depth and are qualitatively consistent with radiative climate models. Localised heating of the tropospheric hazes (100-250 mbar) create a distinct perturbation to the temperature profile that shifts in magnitude and location, declining in the autumn hemisphere and growing in the spring. Changes in the para-H$_2$ ($f_p$) distribution are subtle, with a 0.02-0.03 rise over the spring hemisphere (200-500 mbar) perturbed by (i) low-$f_p$ air advected by both the springtime storm of 2010 and equatorial upwelling; and (ii) subsidence of high-$f_p$ air at northern high latitudes, responsible for a developing north-south asymmetry in $f_p$. Conversely, the shifting asymmetry in the para-H$_2$ disequilibrium primarily reflects the changing temperature structure (and the equilibrium distribution of $f_p$), rather than actual changes in $f_p$ induced by chemical conversion or transport. CIRS results interpolated to the same point in the seasonal cycle as re-analysed Voyager-1 observations show qualitative consistency, with the exception of the tropical tropopause near the equatorial zones and belts, where downward propagation of a cool temperature anomaly associated with Saturn's stratospheric oscillation could potentially perturb tropopause temperatures, para-H$_2$ and winds. [ABRIDGED]Comment: Preprint accepted for publication in Icarus, 29 pages, 18 figure

On the potential of the EChO mission to characterise gas giant atmospheres

Space telescopes such as EChO (Exoplanet Characterisation Observatory) and JWST (James Webb Space Telescope) will be important for the future study of extrasolar planet atmospheres. Both of these missions are capable of performing high sensitivity spectroscopic measurements at moderate resolutions in the visible and infrared, which will allow the characterisation of atmospheric properties using primary and secondary transit spectroscopy. We use the NEMESIS radiative transfer and retrieval tool (Irwin et al. 2008, Lee et al. 2012) to explore the potential of the proposed EChO mission to solve the retrieval problem for a range of H2-He planets orbiting different stars. We find that EChO should be capable of retrieving temperature structure to ~200 K precision and detecting H2O, CO2 and CH4 from a single eclipse measurement for a hot Jupiter orbiting a Sun-like star and a hot Neptune orbiting an M star, also providing upper limits on CO and NH3. We provide a table of retrieval precisions for these quantities in each test case. We expect around 30 Jupiter-sized planets to be observable by EChO; hot Neptunes orbiting M dwarfs are rarer, but we anticipate observations of at least one similar planet.Comment: 22 pages, 30 figures, 4 tables. Accepted for publication in MNRA

Exoplanet atmospheres with EChO: spectral retrievals using EChOSim

We demonstrate the effectiveness of the Exoplanet Characterisation Observatory mission concept for constraining the atmospheric properties of hot and warm gas giants and super Earths. Synthetic primary and secondary transit spectra for a range of planets are passed through EChOSim (Waldmann & Pascale 2014) to obtain the expected level of noise for different observational scenarios; these are then used as inputs for the NEMESIS atmospheric retrieval code and the retrieved atmospheric properties (temperature structure, composition and cloud properties) compared with the known input values, following the method of Barstow et al. (2013a). To correctly retrieve the temperature structure and composition of the atmosphere to within 2 {\sigma}, we find that we require: a single transit or eclipse of a hot Jupiter orbiting a sun-like (G2) star at 35 pc to constrain the terminator and dayside atmospheres; 20 transits or eclipses of a warm Jupiter orbiting a similar star; 10 transits/eclipses of a hot Neptune orbiting an M dwarf at 6 pc; and 30 transits or eclipses of a GJ1214b-like planet.Comment: 13 pages, 15 figures, 1 table. Accepted by Experimental Astronomy. The final publication will shortly be available at Springer via http://dx.doi.org/10.1007/s10686-014-9397-

On the Z_2 Monopole of Spin(10) Gauge Theories

An "expanded" description is introduced to examine the spinor-monopole identification proposed by Strassler for four-dimensional $\cal N$ = 1 supersymmetric Spin(10) gauge theories with matter in F vector and N spinor representations. It is shown that a Z_2 monopole in the "expanded" theory is associated with massive spinors of the Spin(10) theory. For N=2, two spinor case, we confirm this identification by matching the transformation properties of the two theories under SU(2) flavor symmetry. However, for N $\ge$ 3, the transformation properties are not matched between the spinors and the monopole. This disagreement might be due to the fact that the SU(N) flavor symmetry of the Spin(10) theory is partially realized as an SU(2) symmetry in the "expanded" theory.Comment: 16 pages, LaTex, no figur

A Comment on Zero-brane Quantum Mechanics

We consider low energy, non-relativistic scattering of two Dirichlet zero-branes as an exercise in quantum mechanics. For weak string coupling and sufficiently small velocity, the dynamics is governed by an effective U(2) gauge theory in 0+1 dimensions. At low energies, D-brane scattering can reliably probe distances much shorter than the string scale. The only length scale in the quantum mechanics problem is the eleven dimensional Planck length. This provides evidence for the role of scales shorter than the string length in the weakly coupled dynamics of type IIA strings.Comment: 9 pages, harvmac, improved treatment of 2+1 proble