Spatial pair correlations of atoms in molecular dissociation

We perform first-principles quantum simulations of dissociation of trapped, spatially inhomogeneous Bose-Einstein condensates of molecular dimers. Specifically, we study spatial pair correlations of atoms produced in dissociation after time of flight. We find that the observable correlations may significantly degrade in systems with spatial inhomogeneity compared to the predictions of idealized uniform models. We show how binning of the signal can enhance the detectable correlations and lead to the violation of the classical Cauchy-Schwartz inequality and relative number squeezing.Comment: Final published versio

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with non-opposite momenta. The net effect of this process -- which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion -- is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode-mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.Comment: Final published version, with updated references and minor modification

Chiral Perturbation Theory Analysis of the Baryon Magnetic Moments

Nonanalytic $m_q^{1/2}$ and $m_q\ln m_q$ chiral corrections to the baryon magnetic moments are computed. The calculation includes contributions from both intermediate octet and decuplet baryon states. Unlike the one-loop contributions to the baryon axial currents and masses, the contribution from decuplet intermediate states does not partially cancel that from octet intermediate states. The fit to the observed magnetic moments including $m_q^{1/2}$ corrections is found to be much worse than the tree level SU(3) fit if values for the baryon-pion axial coupling constants obtained from a tree level extraction are used. Using the axial coupling constant values extracted at one loop results in a better fit to the magnetic moments than the tree level SU(3) fit. There are three linear relations amongst the magnetic moments when $m_q^{1/2}$ corrections are included, and one relation including $m_q^{1/2}$, $m_q\ln m_q$ and $m_q$ corrections. These relations are independent of the axial coupling constants of the baryons and agree well with experiment.Comment: (16 pages, 2 figures; uses harvmac and uufiles), CERN-TH.6735/92, UCSD/PTH 92-3

Equivariant map superalgebras

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of $X$ is finitely generated, $\Gamma$ is finite abelian and acts freely on the rational points of $X$, and $\mathfrak{g}$ is a basic classical Lie superalgebra (or $\mathfrak{sl}(n,n)$, $n > 0$, if $\Gamma$ is trivial). We show that they are all (tensor products of) generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on $X$. Furthermore, in the case that the even part of $\mathfrak{g}$ is semisimple, we show that all such modules are in fact (tensor products of) evaluation modules. On the other hand, if the even part of $\mathfrak{g}$ is not semisimple (more generally, if $\mathfrak{g}$ is of type I), we introduce a natural generalization of Kac modules and show that all irreducible finite dimensional modules are quotients of these. As a special case, our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras.Comment: 27 pages. v2: Section numbering changed to match published version. Other minor corrections. v3: Minor corrections (see change log at end of introduction

Flash ionization of the partially ionized wind of the progenitor of SN 1987A

The H II region created by the progenitor of SN 1987A was further heated and ionized by the supernova flash. Prior to the flash, the temperature of the gas was 4000 - 5000 K, and helium was neutral, while the post-flash temperature was only slightly less than 10^5 K, with the gas being ionized to helium-like ionization stages of C, N and O. We have followed the slow post-flash cooling and recombination of the gas, as well as its line emission, and find that the strongest lines are N V 1240 and O VI 1034. Both these lines are good probes for the density of the gas, and suitable instruments to detect the lines are STIS on HST and FUSE, respectively. Other lines which may be detectable are N IV] 1486 and [O III] 5007, though they are expected to be substantially weaker. The relative strength of the oxygen lines is found to be a good tracer of the color temperature of the supernova flash. From previous observations, we put limits on the hydrogen density, n_H, of the H II region. The early N V 1240 flux measured by IUE gives an upper limit which is n_H ~ 180 \eta^{-0.40} cm^{-3}, where \eta is the filling factor of the gas. The recently reported emission in [O III] 5007 at 2500 days requires n_H = (160\pm12) \eta^{-0.19} cm^{-3}, for a supernova burst similar to that in the 500full1 model of Ensman & Burrows (1992). For the more energetic 500full2 burst the density is n_H = (215\pm15) \eta^{-0.19} cm^{-3}. These values are much higher than in models of the X-ray emission from the supernova (n_H ~ 75 cm^{-3}), and it seems plausible that the observed [O III] emission is produced primarily elsewhere than in the H II region. We also discuss the type of progenitor consistent with the H II region. In particular, it seems unlikely that its spectral type was much earlier than B2 Ia.Comment: LaTeX, 23 pages including 4 figures. To appear in ApJ (Main Journal

Extensions and block decompositions for finite-dimensional representations of equivariant map algebras

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible finite-dimensional representations of these algebras were classified in previous work with P. Senesi, where it was shown that they are all tensor products of evaluation representations and one-dimensional representations. In the current paper, we describe the extensions between irreducible finite-dimensional representations of an equivariant map algebra in the case that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive. This allows us to also describe explicitly the blocks of the category of finite-dimensional representations in terms of spectral characters, whose definition we extend to this general setting. Applying our results to the case of generalized current algebras (the case where the group acting is trivial), we recover known results but with very different proofs. For (twisted) loop algebras, we recover known results on block decompositions (again with very different proofs) and new explicit formulas for extensions. Finally, specializing our results to the case of (twisted) multiloop algebras and generalized Onsager algebras yields previously unknown results on both extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match published versio

Site response from incident Pnl waves

We developed a new method of determining site response and amplification for use in hazard analysis and station corrections. The method employs the conversion of P to S energy beneath a soft-rock station, which results in complex receiver functions that are frequency and amplitude dependent. At low frequencies (0.5 Hz) can be normalized to these low-frequency levels to quantify the amount of high-frequency amplification. Our results agree with previous studies of the Los Angeles Basin and provide the means of calibrating station responses at high frequencies

Kursk Explosion

On 12 August 2000 two explosions damaged the Russian submarine, the Kursk. The largest event was well recorded at seismic networks in northern Europe, which we then modeled. We developed a hybrid method based on generalized ray theory that treats an explosive source embedded in a fluid and recorded along continental paths. Matching record sections of observations with synthetics, we obtain an estimate of explosive size of slightly over 4 t. Several earth models determined previously, K8 and a Baltic model, were used to assess accuracy. These results are in general agreement with other investigators using more empirical methods. Knowing the conventional missile yield and the explosion size allows for an estimate of approximately five missiles exploded in the second larger explosion onboard the Kursk

On Characterizing the Data Access Complexity of Programs

Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a fundamental characterization of data access complexity will be increasingly important. The problem of developing lower bounds for data access complexity has been modeled using the formalism of Hong & Kung's red/blue pebble game for computational directed acyclic graphs (CDAGs). However, previously developed approaches to lower bounds analysis for the red/blue pebble game are very limited in effectiveness when applied to CDAGs of real programs, with computations comprised of multiple sub-computations with differing DAG structure. We address this problem by developing an approach for effectively composing lower bounds based on graph decomposition. We also develop a static analysis algorithm to derive the asymptotic data-access lower bounds of programs, as a function of the problem size and cache size