Geodesic distances on density matrices

We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.Comment: 10 page

Connections and Metrics Respecting Standard Purification

Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.Comment: Latex, 27 page

On the Apparent Orbital Inclination Change of the Extrasolar Transiting Planet TrES-2b

On June 15, 2009 UT the transit of TrES-2b was detected using the University of Arizona's 1.55 meter Kuiper Telescope with 2.0-2.5 millimag RMS accuracy in the I-band. We find a central transit time of $T_c = 2454997.76286 \pm0.00035$ HJD, an orbital period of $P = 2.4706127 \pm 0.0000009$ days, and an inclination angle of $i = 83^{\circ}.92 \pm 0.05$, which is consistent with our re-fit of the original I-band light curve of O'Donovan et al. (2006) where we find $i = 83^{\circ}.84 \pm0.05$. We calculate an insignificant inclination change of $\Delta i = -0^{\circ}.08 \pm 0.07$ over the last 3 years, and as such, our observations rule out, at the $\sim 11 \sigma$ level, the apparent change of orbital inclination to $i_{predicted} = 83^{\circ}.35 \pm0.1$ as predicted by Mislis and Schmitt (2009) and Mislis et al. (2010) for our epoch. Moreover, our analysis of a recently published Kepler Space Telescope light curve (Gilliland et al. 2010) for TrES-2b finds an inclination of $i = 83^{\circ}.91 \pm0.03$ for a similar epoch. These Kepler results definitively rule out change in $i$ as a function of time. Indeed, we detect no significant changes in any of the orbital parameters of TrES-2b.Comment: 19 pages, 1 table, 7 figures. Re-submitted to ApJ, January 14, 201

A Revised Orbital Ephemeris for HAT-P-9b

We present here three transit observations of HAT-P-9b taken on 14 February 2010, 18 February 2010, and 05 April 2010 UT from the University of Arizona's 1.55 meter Kuiper telescope on Mt. Bigelow. Our transit light curves were obtained in the I filter for all our observations, and underwent the same reduction process. All three of our transits deviated significantly (approximately 24 minutes earlier) from the ephemeris of Shporer et al. (2008). However, due to the large time span between our observed transits and those of Shporer et al. (2008), a 6.5 second (2 sigma) shift downwards in orbital period from the value of Shporer et al. (2008) is sufficient to explain all available transit data. We find a new period of 3.922814 +/- 0.000002 days for HAT-P-9b with no evidence for significant nonlinearities in the transit period.Comment: 10 pages, 3 figure

Trigonometric Parallaxes for 1,507 Nearby Mid-to-Late M-dwarfs

The MEarth survey is a search for small rocky planets around the smallest, nearest stars to the Sun as identified by high proper motion with red colors. We augmented our planetary search time series with lower cadence astrometric imaging and obtained two million images of approximately 1800 stars suspected to be mid-to-late M dwarfs. We fit an astrometric model to MEarth's images for 1507 stars and obtained trigonometric distance measurements to each star with an average precision of 5 milliarcseconds. Our measurements, combined with the 2MASS photometry, allowed us to obtain an absolute K_s magnitude for each star. In turn, this allows us to better estimate the stellar parameters than those obtained with photometric estimates alone and to better prioritize the targets chosen to monitor at high cadence for planetary transits. The MEarth sample is mostly complete out to a distance of 25 parsecs for stars of type M5.5V and earlier, and mostly complete for later type stars out to 20 parsecs. We find eight stars that are within ten parsecs of the Sun for which there did not exist a published trigonometric parallax distance estimate. We release with this work a catalog of the trigonometric parallax measurements for 1,507 mid-to-late M-dwarfs, as well as new estimates of their masses and radii.Comment: ApJ, accepted. 36 pages, 8 figures, 2 tables. Please find our data table here: http://www.cfa.harvard.edu/MEarth/DataDR2.htm

Clozapine as add-on medication in the maintenance treatment of bipolar and schizoaffective disorders - A case series

Atypical neuroleptics are increasingly used in the treatment of bipolar and schizoaffective disorders. Currently, numerous controlled short-term studies are available for clozapine, olanzapine, risperidone or quetiapine, but long-term data are still missing. Three patients (2 with bipolar disorder, 1 with schizoaffective disorder) are described who showed a marked reduction of affective symptomatology after clozapine had been added to mood stabilizer pretreatment. The patients were seen once a month before and after the introduction of clozapine for at least 6 months. Treatment response was evaluated using different rating scales (IDS, YMRS; GAF; CGIBP) and the NIMH Life Chart Methodology. All patients showed a marked improvement after the add-on treatment with clozapine had been initiated. Clozapine was tolerated well with only transient and moderate weight gain and fatigue as only side effects. This case series underlines the safety and efficacy of clozapine as add-on medication in the treatment of bipolar and schizoaffective disorders. Copyright (C) 2002 S. Karger AG, Basel

The rotation and Galactic kinematics of mid M dwarfs in the Solar Neighborhood

Rotation is a directly-observable stellar property, and drives magnetic field generation and activity through a magnetic dynamo. Main sequence stars with masses below approximately 0.35Msun (mid-to-late M dwarfs) are fully-convective, and are expected to have a different type of dynamo mechanism than solar-type stars. Measurements of their rotation rates provide insights into these mechanisms, but few rotation periods are available for these stars at field ages. Using photometry from the MEarth transit survey, we measure rotation periods for 387 nearby, mid-to-late M dwarfs in the Northern hemisphere, finding periods from 0.1 to 140 days. The typical detected rotator has stable, sinusoidal photometric modulations at a semi-amplitude of 0.5 to 1%. We find no period-amplitude relation for stars below 0.25Msun and an anti-correlation between period and amplitude for higher-mass M dwarfs. We highlight the existence of older, slowly-rotating stars without H{\alpha} emission that nevertheless have strong photometric variability. The Galactic kinematics of our sample is consistent with the local population of G and K dwarfs, and rotators have metallicities characteristic of the Solar Neighborhood. We use the W space velocities and established age-velocity relations to estimate that stars with P<10 days are on average <2 Gyrs, and that those with P>70 days are about 5 Gyrs. The period distribution is mass dependent: as the mass decreases, the slowest rotators at a given mass have longer periods, and the fastest rotators have shorter periods. We find a lack of stars with intermediate rotation periods. [Abridged]Comment: Accepted to ApJ. Machine readable tables and additional figures are available in the published article or on reques

A Tentative Detection of a Starspot During Consecutive Transits of an Extrasolar Planet from the Ground: No Evidence of a Double Transiting Planet System Around TrES-1

There have been numerous reports of anomalies during transits of the planet TrES-1b. Recently, Rabus and coworkers' analysis of HST observations lead them to claim brightening anomalies during transit might be caused by either a second transiting planet or a cool starspot. Observations of two consecutive transits are presented here from the University of Arizona's 61-inch Kuiper Telescope on May 12 and May 15, 2008 UT. A 5.4 +/- 1.7 mmag (0.54 +/- 0.17%) brightening anomaly was detected during the first half of the transit on May 12 and again in the second half of the transit on May 15th. We conclude that this is a tentative detection of a r greater than or equal to 6 earth radii starspot rotating on the surface of the star. We suggest that all evidence to date suggest TrES-1 has a spotty surface and there is no need to introduce a second transiting planet in this system to explain these anomalies. We are only able to constrain the rotational period of the star to 40.2 +22.9 -14.6 days, due to previous errors in measuring the alignment of the stellar spin axis with the planetary orbital axis. This is consistent with the previously observed P_obs = 33.2 +22.3 -14.3 day period. We note that this technique could be applied to other transiting systems for which starspots exist on the star in the transit path of the planet in order to constrain the rotation rate of the star. (abridged)Comment: 21 pages, 3 tables, 6 figures, Accepted to Ap