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

Rates of mixing for the measure of maximal entropy of dispersing billiard maps

In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic properties for H\"older continuous observables, such as at least polynomial decay of correlations and the Central Limit Theorem. The results of Baladi and Demers are subject to a condition of sparse recurrence to singularities. We use a similar and slightly stronger condition, and it has a direct effect on our rate of decay of correlations. For billiard tables with bounded complexity (a property conjectured to be generic), we show that the sparse recurrence condition is always satisfied and the correlations decay at a super-polynomial rate

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

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

Stellar populations in the dwarf spheroidal galaxy Leo I

We present a detailed study of the color magnitude diagram (CMD) of the dwarf spheroidal galaxy Leo I, based on archival Hubble Space Telescope data. Our photometric analysis, confirming previous results on the brighter portion of the CMD, allow us to obtain an accurate sampling of the stellar populations also at the faint magnitudes corresponding to the Main Sequence. By adopting a homogeneous and consistent theoretical scenario for both hydrogen and central helium-burning evolutionary phases, the various features observed in the CMD are interpreted and reliable estimations for both the distance modulus and the age(s) for the main stellar components of Leo I are derived. More in details, from the upper luminosity of the Red Giant Branch and the lower luminosity of the Subgiant Branch we simultaneously constrain the galaxy distance and the age of the oldest stellar population in Leo I. In this way we obtain a distance modulus (m-M)_V=22.00$\pm$0.15 mag and an age of 10--15 Gyr or 9--13 Gyr, adopting a metallicity Z=0.0001 and 0.0004, respectively. The reliability of this distance modulus has been tested by comparing the observed distribution of the Leo I anomalous Cepheids in the period-magnitude diagram with the predicted boundaries of the instability strip, as given by convective pulsating models.Comment: 19 pages, 3 tables, 14 figures To be published in A