A quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices

We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photon-counting probability when measuring a linear-optically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithms development.Comment: 9 pages, 1 figure. Updated version for publicatio

Kalikow-type decomposition for multicolor infinite range particle systems

We consider a particle system on $\mathbb{Z}^d$ with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an algorithm to obtain an explicit construction of a coupling attaining Ornstein's $\bar{d}$-distance for two ordered Ising probability measures.Comment: Published in at http://dx.doi.org/10.1214/12-AAP882 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantum spin Hall phase in multilayer graphene

The so called quantum spin Hall phase is a topologically non trivial insulating phase that is predicted to appear in graphene and graphene-like systems. In this work we address the question of whether this topological property persists in multilayered systems. We consider two situations: purely multilayer graphene and heterostructures where graphene is encapsulated by trivial insulators with a strong spin-orbit coupling. We use a four orbital tight-binding model that includes the full atomic spin-orbit coupling and we calculate the $Z_{2}$ topological invariant of the bulk states as well as the edge states of semi-infinite crystals with armchair termination. For homogeneous multilayers we find that even when the spin-orbit interaction opens a gap for all the possible stackings, only those with odd number of layers host gapless edge states while those with even number of layers are trivial insulators. For the heterostructures where graphene is encapsulated by trivial insulators, it turns out that the interlayer coupling is able to induce a topological gap whose size is controlled by the spin-orbit coupling of the encapsulating materials, indicating that the quantum spin Hall phase can be induced by proximity to trivial insulators.Comment: 7 pages, 6 figure

Dust Around R Coronae Borealis Stars. I. Spitzer/Infrared Spectrograph Observations

Spitzer/infrared spectrograph (IRS) spectra from 5 to 37 mu m for a complete sample of 31 R Coronae Borealis stars (RCBs) are presented. These spectra are combined with optical and near-infrared photometry of each RCB at maximum light to compile a spectral energy distribution (SED). The SEDs are fitted with blackbody flux distributions and estimates are made of the ratio of the infrared flux from circumstellar dust to the flux emitted by the star. Comparisons for 29 of the 31 stars are made with the Infrared Astronomical Satellite (IRAS) fluxes from three decades earlier: Spitzer and IRAS fluxes at 12 mu m and 25 mu m are essentially equal for all but a minority of the sample. For this minority, the IRAS to Spitzer flux ratio exceeds a factor of three. The outliers are suggested to be stars where formation of a dust cloud or dust puff is a rare event. A single puff ejected prior to the IRAS observations may have been reobserved by Spitzer as a cooler puff at a greater distance from the RCB. RCBs which experience more frequent optical declines have, in general, a circumstellar environment containing puffs subtending a larger solid angle at the star and a quasi-constant infrared flux. Yet, the estimated subtended solid angles and the blackbody temperatures of the dust show a systematic evolution to lower solid angles and cooler temperatures in the interval between IRAS and Spitzer. Dust emission by these RCBs and those in the LMC is similar in terms of total 24 mu m luminosity and [8.0]-[24.0] color index.Spanish Ministry of Science and Innovation (MICINN) AYA-2007-64748NASA GO 50212, 1407Robert A. Welch Foundation of Houston, Texas F-634McDonald Observator

High-resolution optical spectroscopy of DY Cen: diffuse interstellar bands in a proto-fullerene circumstellar environment?

We search high-resolution and high-quality VLT/UVES optical spectra of the hot R Coronae Borealis (RCB) star DY Cen for electronic transitions of the C60 molecule and diffuse interstellar bands (DIBs). We report the non-detection of the strongest C60 electronic transitions (e.g., those at ~3760, 3980, and 4024 A). Absence of C60 absorption bands may support recent laboratory results, which show that the ~7.0, 8.5, 17.4, and 18.8 um emission features seen in DY Cen - and other similar objects with PAH-like dominated IR spectra - are attributable to proto-fullerenes or fullerene precursors rather than to C60. DIBs towards DY Cen are normal for its reddening; the only exception is the DIB at 6284 A (possibly also the 7223A DIB) that is found to be unusually strong. We also report the detection of a new broad (FWHM~2 A) and unidentified feature centered at ~4000 A. We suggest that this new band may be related to the circumstellar proto-fullerenes seen at infrared wavelengths.Comment: Accepted for publication in The Astrophysical Journal Letters (15 pages, 3 figures, and 2 tables

Superburst oscillations: ocean and crustal modes excited by Carbon-triggered Type I X-ray bursts

Accreting neutron stars (NS) can exhibit high frequency modulations in their lightcurves during thermonuclear X-ray bursts, known as burst oscillations. The frequencies can be offset from the spin frequency of the NS by several Hz, and can drift by 1-3 Hz. One possible explanation is a mode in the bursting ocean, the frequency of which would decrease (in the rotating frame) as the burst cools, hence explaining the drifts. Most burst oscillations have been observed during H/He triggered bursts, however there has been one observation of oscillations during a superburst; hours' long Type I X-ray bursts caused by unstable carbon burning deeper in the ocean. This paper calculates the frequency evolution of an oceanic r-mode during a superburst. The rotating frame frequency varies during the burst from 4-14 Hz, and is sensitive to the background parameters, in particular the temperature of the ocean and ignition depth. This calculation is compared to the superburst oscillations observed on 4U-1636-536. The predicted mode frequencies ($\sim$ 10 Hz) would require a spin frequency of $\sim$ 592 Hz to match observations; 6 Hz higher than the spin inferred from an oceanic r-mode model for the H/He triggered burst oscillations. This model also over-predicts the frequency drift during the superburst by 90 %.Comment: Accepted for publication in MNRA