Beltway: Getting Around Garbage Collection Gridlock

We present the design and implementation of a new garbage collection framework that significantly generalizes existing copying collectors. The Beltway framework exploits and separates object age and incrementality. It groups objects in one or more increments on queues called belts, collects belts independently, and collects increments on a belt in first-in-first-out order. We show that Beltway configurations, selected by command line options, act and perform the same as semi-space, generational, and older-first collectors, and encompass all previous copying collectors of which we are aware. The increasing reliance on garbage collected languages such as Java requires that the collector perform well. We show that the generality of Beltway enables us to design and implement new collectors that are robust to variations in heap size and improve total execution time over the best generational copying collectors of which we are aware by up to 40%, and on average by 5 to 10%, for small to moderate heap sizes. New garbage collection algorithms are rare, and yet we define not just one, but a new family of collectors that subsumes previous work. This generality enables us to explore a larger design space and build better collectors

Non-Abelian Fractional Chern Insulators from Long-Range Interactions

The recent theoretical discovery of fractional Chern insulators (FCIs) has provided an important new way to realize topologically ordered states in lattice models. In earlier works, on-site and nearest neighbor Hubbard-like interactions have been used extensively to stabilize Abelian FCIs in systems with nearly flat, topologically nontrivial bands. However, attempts to use two-body interactions to stabilize non-Abelian FCIs, where the ground state in the presence of impurities can be massively degenerate and manipulated through anyon braiding, have proven very difficult in uniform lattice systems. Here, we study the remarkable effect of long-range interactions in a lattice model that possesses an exactly flat lowest band with a unit Chern number. When spinless bosons with two-body long-range interactions partially fill the lowest Chern band, we find convincing evidence of gapped, bosonic Read-Rezayi (RR) phases with non-Abelian anyon statistics. We characterize these states through studying topological degeneracies, the overlap between the ground states of two-body interactions and the exact RR ground states of three- and four-body interactions, and state counting in the particle-cut entanglement spectrum. Moreover, we demonstrate how an approximate lattice form of Haldane's pseudopotentials, analogous to that in the continuum, can be used as an efficient guiding principle in the search for lattice models with stable non-Abelian phases.Comment: 12 pages, 7 figures. As publishe

Tidal Excitation of Modes in Binary Systems with Applications to Binary Pulsars

We consider the tidal excitation of modes in a binary system of arbitrary eccentricity. For a circular orbit, the modes generally undergo forced oscillation with a period equal to the orbital period ($T$). For an eccentric orbit, the amplitude of each tidally excited mode can be written approximately as the sum of an oscillatory term that varies sinusoidally with the mode frequency and a `static' term that follows the time dependence of the tidal forcing function. The oscillatory term falls off exponentially with increasing \b (defined as the ratio of the periastron passage time to the mode period), whereas the `static' term is independent of \b. For small \b modes (\b \approx 1), the two terms are comparable, and the magnitude of the mode amplitude is nearly constant over the orbit. For large \b modes (\b \gta a few), the oscillatory term is very small compared to the `static' term, in which case the mode amplitude, like the tidal force, varies as the distance cubed. For main sequence stars, $p$, $f$, and low order $g$-modes generally have large \b and hence small amplitudes of oscillation. High overtone $g$-modes, however, have small overlap with the tidal forcing function. Thus, we expect an intermediate overtone $g$-mode with \b \sim 1 to have the largest oscillation amplitude. The dependence on mode damping and the stellar rotation rate is considered, as well as the effects of orbital evolution. We apply our work to the two binary pulsar system: PSR J0045-7319 and PSR B1259-63.Comment: 28 pages of uuencoded compressed postscript. 9 postscript figures available by anonymous ftp from ftp://brmha.mit.edu/ To be published in ApJ

Even-Odd Correlation Functions on an Optical Lattice

We study how different many body states appear in a quantum gas microscope, such as the one developed at Harvard [Bakr et al. Nature 462, 74 (2009)], where the site-resolved parity of the atom number is imaged. We calculate the spatial correlations of the microscope images, corresponding to the correlation function of the parity of the number of atoms at each site. We produce analytic results for a number of well-known models: noninteracting bosons, the large U Bose-Hubbard model, and noninteracting fermions. We find that these parity correlations tend to be less strong than density-density correlations, but they carry similar information.Comment: 8 pages, 4 figures. Published versio

Differential rotation enhanced dissipation of tides in the PSR J0045-7319 Binary

Recent observations of PSR J0045-7319, a radio pulsar in a close eccentric orbit with a massive B-star companion, indicate that the system's orbital period is decreasing on a timescale of $\approx 5 \times10^{5}$ years, which is much shorter than the timescale of $\approx$ 10^9 years given by the standard theory of tidal dissipation in radiative stars. Observations also provide strong evidence that the B-star is rotating rapidly, perhaps at nearly its break up speed. We show that the dissipation of the dynamical tide in a star rotating in the same direction as the orbital motion of its companion (prograde rotation) with a speed greater than the orbital angular speed of the star at periastron results in an increase in the orbital period of the binary system with time. Thus, since the observed time derivative of the orbital period is large and negative, the B-star in the PSR J0045-7319 binary must have retrograde rotation if tidal effects are to account for the orbital decay. We also show that the time scale for the synchronization of the B-star's spin with the orbital angular speed of the star at periastron is comparable to the orbital evolution time. From the work of Goldreich and Nicholson (1989) we therefore expect that the B-star should be rotating differentially, with the outer layers rotating more slowly than the interior. We show that the dissipation of the dynamical tide in such a differentially rotating B-star is enhanced by almost three orders of magnitude leading to an orbital evolution time for the PSR J0045-7319 Binary that is consistent with the observations.Comment: 8 pages, tex. Submitted to Ap