Loschmidt echo and fidelity decay near an exceptional point

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi

Phase transitions and generalized biorthogonal polarization in non-Hermitian systems

Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, notably including systems with gain and loss, and are currently intensively studied in the context of topology. A salient difference between Hermitian and NH models is the breakdown of the conventional bulk-boundary correspondence, invalidating the use of topological invariants computed from the Bloch bands to characterize boundary modes in generic NH systems. One way to overcome this difficulty is to use the framework of biorthogonal quantum mechanics to define a biorthogonal polarization, which functions as a real-space invariant signaling the presence of boundary states. Here, we generalize the concept of the biorthogonal polarization beyond the previous results to systems with any number of boundary modes and show that it is invariant under basis transformations as well as local unitary transformations. Additionally, we focus on the anisotropic Su-Schrieffer-Heeger chain and study gap closings analytically. We also propose a generalization of a previously developed method with which to find all the bulk states of the system with open boundaries to NH models. Using the exact solutions for the bulk and boundary states, we elucidate genuinely NH aspects of the interplay between the bulk and boundary at the phase transitions

Extended Stromgren Photoelectric Photometry in NGC 752

Photoelectric photometry on the extended Stromgren system (uvbyCa) is presented for 7 giants and 21 main sequence stars in the old open cluster, NGC 752. Analysis of the hk data for the turnoff stars yields a new determination of the cluster mean metallicity. From 10 single-star members, [Fe/H] = -0.06 +/- 0.03, where the error quoted is the standard error of the mean and the Hyades abundance is set at [Fe/H] = +0.12. This result is unchanged if all 20 stars within the limits of the hk metallicity calibration are included. The derived [Fe/H] is in excellent agreement with past estimates using properly-zeroed m1 data, transformed moderate-dispersion spectroscopy, and recent high dispersion spectroscopy.Comment: 14 tex'd pages including 2 tables; 2 separate files with eps figures Accepted for PASP March 200

The Southern Proper Motion Program III. A Near-Complete Catalog to V=17.5

We present the third installment of the Yale/San Juan Southern Proper Motion Catalog, SPM3. Absolute proper motions, positions, and photographic B,V photometry are given for roughly 10.7 million objects, primarily stars, down to a magnitude of V=17.5. The Catalog covers an irregular area of 3700 square degrees, between the declinations of -20 and -45 degrees, excluding the Galactic plane. The proper-motion precision, for well-measured stars, is estimated to be 4.0 mas/yr. Unlike previous releases of the SPM Catalog, the proper motions are on the International Celestial Reference System by way of Hipparcos Catalog stars, and have an estimated systematic uncertainty of 0.4 mas/yr. The SPM3 Catalog is available via electronic transfer,(http://www.astro.yale.edu/astrom/) As an example of the potential of the SPM3 proper motions, we examine the Galactocentric velocities of a group of metal-poor, main-sequence A stars. The majority of these exhibit thick-disk kinematics, lending support to their interpretation as thick-disk blue stragglers, as opposed to being an accreted component.Comment: 23 pages, 10 figures, accepted for publication in Astronomical Journa

The First Galaxies: Clues from Element Abundances

It has recently become possible to measure directly the abundances of several chemical elements in a variety of environments at redshifts up to z = 5. In this review I summarise the latest observations of Lyman break galaxies, damped Lyman alpha systems and the Lyman alpha forest with a view to uncovering any clues which these data may offer to the first episodes of star formation. The picture which is emerging is one where the universe at z = 3 already included many of the components of today's galaxies--even at these early times we see evidence for Populations I and II stars, while the `smoking gun' for Population III objects may be hidden in the chemical composition of the lowest density regions of the IGM, yet to be deciphered.Comment: 15 pages, LaTex, 8 Postscript Figures. To appear in the Philosophical Transactions of The Royal Society, Series

A Simple Model for r-Process Scatter and Halo Evolution

Recent observations of heavy elements produced by rapid neutron capture (r-process) in the halo have shown a striking and unexpected behavior: within a single star, the relative abundances of r-process elements heavier than Eu are the same as the same as those of solar system matter, while across stars with similar metallicity Fe/H, the r/Fe ratio varies over two orders of magnitude. In this paper we present a simple analytic model which describes a star's abundances in terms of its ``ancestry,'' i.e., the number of nucleosynthesis events (e.g., supernova explosions) which contributed to the star's composition. This model leads to a very simple analytic expression for the abundance scatter versus Fe/H, which is in good agreement with the data and with more sophisticated numerical models. We investigate two classes of scenarios for r-process nucleosynthesis, one in which r-process synthesis events occur in only \sim 4% of supernovae but iron synthesis is ubiquitous, and one in which iron nucleosynthesis occurs in only about 9% of supernovae. (the Wasserburg- Qian model). We find that the predictions in these scenarios are similar for [Fe/H] \ga -2.5, but that these models can be readily distinguished observationally by measuring the dispersion in r/Fe at [Fe/H] \la -3.Comment: AASTeX, 21 pages, includes 4 figure

On Variations in the Peak Luminosity of Type Ia Supernovae

We explore the idea that the observed variations in the peak luminosities of Type Ia supernovae originate in part from a scatter in metallicity of the main-sequence stars that become white dwarfs. Previous, numerical, studies have not self-consistently explored metallicities greater than solar. One-dimensional Chandrasekhar mass models of SNe Ia produce most of their 56Ni in a burn to nuclear statistical equilibrium between the mass shells 0.2 and 0.8 solar masses, for which the electron to nucleon ratio is constant during the burn. We show analytically that, under these conditions, charge and mass conservation constrain the mass of 56Ni produced to depend linearly on the original metallicity of the white dwarf progenitor. Detailed post-processing of W7-like models confirms this linear dependence. The effect that we identify is most evident at metallicities larger than solar, and is in agreement with previous self-consistent calculations over the metallicity range common to both calculations. The observed scatter in the metallicity (1/3--3 times solar) of the solar neighborhood is enough to induce a 25% variation in the mass of 56Ni ejected by Type Ia supernovae. This is sufficient to vary the peak V-band brightness by approximately 0.2. This scatter in metallicity is present out to the limiting redshifts of current observations (z < 1). Sedimentation of 22Ne can possibly amplify the variation in 56Ni mass up to 50%. Further numerical studies can determine if other metallicity-induced effects, such as a change in the mass of the 56Ni-producing region, offset or enhance this variation.Comment: 4 pages, 1 figure, to appear in ApJL. Uses emulateapj.cls (included

Resolving the Formation of Protogalaxies. III. Feedback from the First Stars

The first stars form in dark matter halos of masses ~10^6 M_sun as suggested by an increasing number of numerical simulations. Radiation feedback from these stars expels most of the gas from their shallow potential well of their surrounding dark matter halos. We use cosmological adaptive mesh refinement simulations that include self-consistent Population III star formation and feedback to examine the properties of assembling early dwarf galaxies. Accurate radiative transport is modeled with adaptive ray tracing. We include supernova explosions and follow the metal enrichment of the intergalactic medium. The calculations focus on the formation of several dwarf galaxies and their progenitors. In these halos, baryon fractions in 10^8 solar mass halos decrease by a factor of 2 with stellar feedback and by a factor of 3 with supernova explosions. We find that radiation feedback and supernova explosions increase gaseous spin parameters up to a factor of 4 and vary with time. Stellar feedback, supernova explosions, and H_2 cooling create a complex, multi-phase interstellar medium whose densities and temperatures can span up to 6 orders of magnitude at a given radius. The pair-instability supernovae of Population III stars alone enrich the halos with virial temperatures of 10^4 K to approximately 10^{-3} of solar metallicity. We find that 40% of the heavy elements resides in the intergalactic medium (IGM) at the end of our calculations. The highest metallicity gas exists in supernova remnants and very dilute regions of the IGM.Comment: 15 pages, 16 figures, accepted to ApJ. Many changes, including estimates of metal line cooling. High resolution images and movies available at http://www.slac.stanford.edu/~jwise/research/PGalaxies3