Hermiticity and the Cohomology Condition in Topological Yang-Mills Theory

The symmetries of the topological Yang-Mills theory are studied in the Hamiltonian formalism and the generators of the twisted N=2 superPoincar\'e algebra are explicitly constructed. Noting that the twisted Lorentz generators do not generate the Lorentz symmetry of the theory, we relate the two by extracting from the latter the twisted version of the internal SU(2) generator. The hermiticity properties of the various generators are also considered throughout, and the boost generators are found to be non-hermitian. We then recover the BRST cohomology condition on physical states from representation theory arguments.Comment: 19 pages, MIT-CTP 223

Fluctuations of the Unruh Temperature

Using the influence functional formalism, the problem of an accelerating detector in the presence of a scalar field in its ground state is considered in Minkowski space. As is known since the work of Unruh, to a quantum mechanical detector following a definite, classical acceleration, the field appears to be thermally excited. We relax the requirement of perfect classicality for the trajectory and substitute it with one of {\it derived} classicality through the criteria of decoherence. The ensuing fluctuations in temperature are then related with the time and the amplitude of excitation in the detector's internal degree of freedom.Comment: LATEX, 12 pages + 2 figures (available upon request) MIT-CTP 234

Behavior of the Escape Rate Function in Hyperbolic Dynamical Systems

For a fixed initial reference measure, we study the dependence of the escape rate on the hole for a smooth or piecewise smooth hyperbolic map. First, we prove the existence and Holder continuity of the escape rate for systems with small holes admitting Young towers. Then we consider general holes for Anosov diffeomorphisms, without size or Markovian restrictions. We prove bounds on the upper and lower escape rates using the notion of pressure on the survivor set and show that a variational principle holds under generic conditions. However, we also show that the escape rate function forms a devil's staircase with jumps along sequences of regular holes and present examples to elucidate some of the difficulties involved in formulating a general theory.Comment: 21 pages. v2 differs from v1 only by additions to the acknowledgment

The elusive old population of the dwarf spheroidal galaxy Leo I

We report the discovery of a significant old population in the dwarf spheroidal (dSph) galaxy Leo I as a result of a wide-area search with the ESO New Technology Telescope. Studies of the stellar content of Local Group dwarf galaxies have shown the presence of an old stellar population in almost all of the dwarf spheroidals. The only exception was Leo I, which alone appeared to have delayed its initial star formation episode until just a few Gyr ago. The color-magnitude diagram of Leo I now reveals an extended horizontal branch, unambiguously indicating the presence of an old, metal-poor population in the outer regions of this galaxy. Yet we find little evidence for a stellar population gradient, at least outside R > 2' (0.16 kpc), since the old horizontal branch stars of Leo I are radially distributed as their more numerous intermediate-age helium-burning counterparts. The discovery of a definitely old population in the predominantly young dwarf spheroidal galaxy Leo I points to a sharply defined first epoch of star formation common to all of the Local Group dSph's as well as to the halo of the Milky Way.Comment: 4 pages, 3 postscript figures, uses apjfonts.sty, emulateapj.sty. Accepted for publication in ApJ Letter

Normal-Superfluid Interface Scattering For Polarized Fermion Gases

We argue that, for the recent experiments with imbalanced fermion gases, a temperature difference may occur between the normal (N) and the gapped superfluid (SF) phase. Using the mean-field formalism, we study particle scattering off the N-SF interface from the deep BCS to the unitary regime. We show that the thermal conductivity across the interface drops exponentially fast with increasing $h/k_B T$, where $h$ is the chemical potential imbalance. This implies a blocking of thermal equilibration between the N and the SF phase. We also provide a possible mechanism for the creation of gap oscillations (FFLO-like states) as seen in recent studies on these systems.Comment: 4 pages, 3 figure

Spectral degeneracy and escape dynamics for intermittent maps with a hole

We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show that the absolutely continuous conditional invariant measures (ACCIMs) converge to the ACIM as the length of the small neighbourhood shrinks to zero. We then quantify how the escape dynamics from these almost-invariant sets are connected with the second eigenfunctions of Perron-Frobenius (transfer) operators when a small perturbation is applied near the intermittent fixed point. In particular, we describe precisely the scaling of the second eigenvalue with the perturbation size, provide upper and lower bounds, and demonstrate $L^1$ convergence of the positive part of the second eigenfunction to the ACIM as the perturbation goes to zero. This perturbation and associated eigenvalue scalings and convergence results are all compatible with Ulam's method and provide a formal explanation for the numerical behaviour of Ulam's method in this nonuniformly hyperbolic setting. The main results of the paper are illustrated with numerical computations.Comment: 34 page

Improved photometry of SDSS crowded field images: Structure and dark matter content in the dwarf spheroidal galaxy Leo I

We explore how well crowded field point-source photometry can be accomplished with SDSS data: We present a photometric pipeline based on DoPhot, and tuned for analyzing crowded-field images from the SDSS. Using Monte Carlo simulations we show that the completeness of source extraction is above 80% to i < 21 (AB) and a stellar surface density of about 200 sq.amin. Hence, a specialized data pipeline can efficiently be used for e.g. nearby resolved galaxies in SDSS images, where the standard SDSS photometric package Photo, when applied in normal survey mode, gives poor results. We apply our pipeline to an area of about 3.55sq.deg. around the dwarf spheroidal galaxy (dSph) Leo I, and construct a high S/N star-count map of Leo I via an optimized filter in color-magnitude space (g,r,i). Although the radial surface-density profile of the dwarf deviates from the best fit empirical King model towards outer radii, we find no evidence for tidal debris out to a stellar surface-density of 4*10^(-3) of the central value. We determine the total luminosity of Leo I, and model its mass using the spherical and isotropic Jeans equation. Assuming that 'mass follows light' we constrain a lower limit of the total mass of the dSph to be (1.7+/-0.2)*10^7 Msol. Contrary, if the mass in Leo I is dominated by a constant density dark-matter (DM) halo, then the mass within the central 12' is (2+/-0.6)*10^8 Msol. This leads to a mass-to-light ratio of >>6 (Ic_sol), and possibly >75 if the DM halo dominates the mass and extends further out than 12'. In summary, our results show that Leo I is a symmetric, relaxed and bound system; this supports the idea that Leo I is a dark-matter dominated system.Comment: 13 pages, 11 figures; accepted for publication in A

RR Lyrae stars in four globular clusters in the Fornax dwarf galaxy

(Abridged) We have surveyed four globular clusters in the Fornax dwarf galaxy for RR Lyrae stars, using archival HST observations. We identify 197 new RR Lyrae stars in these four clusters. Despite the short observational baseline, we derive periods, light-curves, and photometric parameters for each. The Fornax clusters have exceptionally large RR Lyrae specific frequencies compared with the Galactic globular clusters. Furthermore, the Fornax cluster RR Lyrae stars are unusual in that their characteristics are intermediate between the two Galactic Oosterhoff groups. In this respect the Fornax clusters are similar to the field populations in several dwarf galaxies. We revise previous measurements of the HB morphology in each cluster. The Fornax clusters closely resemble the ``young'' Galactic halo population defined by Zinn. The existence of the second parameter effect among the Fornax clusters is also confirmed. Finally, we determine foreground reddening and distance estimates for each cluster. We find a mean distance modulus to Fornax of (m-M)_0 = 20.66 +/- 0.03 (random) +/- 0.15 (systematic). Our measurements are consistent with a line of sight depth of 8-10 kpc for this galaxy, matching its projected dimensions, and incompatible with tidal model explanations for the observed high velocity dispersions in many dSph galaxies. Dark matter dominance is suggested.Comment: 26 pages, 6 figures. Accepted for publication in MNRAS. Table 2 and Figure 2 will only be available in the electronic version. On-line data will soon be available at http://www.ast.cam.ac.uk/STELLARPOPS/Fornax_RRlyr