Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Entanglement of zero angular momentum mixtures and black hole entropy

We calculate the entanglement of formation and the entanglement of distillation for arbitrary mixtures of the zero spin states on an arbitrary-dimensional bipartite Hilbert space. Such states are relevant to quantum black holes and to decoherence-free subspaces based communication. The two measures of entanglement are equal and scale logarithmically with the system size. We discuss its relation to the black hole entropy law. Moreover, these states are locally distinguishable but not locally orthogonal, thus violating a conjecture that the entanglement measures coincide only on locally orthogonal states. We propose a slightly weaker form of this conjecture. Finally, we generalize our entanglement analysis to any unitary group.Comment: 5 pages, revtex4 Final version. A discussion of local orthogonality and entanglement is adde

Global water cycle

This research is the MSFC component of a joint MSFC/Pennsylvania State University Eos Interdisciplinary Investigation on the global water cycle extension across the earth sciences. The primary long-term objective of this investigation is to determine the scope and interactions of the global water cycle with all components of the Earth system and to understand how it stimulates and regulates change on both global and regional scales. Significant accomplishments in the past year are presented and include the following: (1) water vapor variability; (2) multi-phase water analysis; (3) global modeling; and (4) optimal precipitation and stream flow analysis and hydrologic processes

Quantum Black Holes: Entropy and Entanglement on the Horizon

We are interested in black holes in Loop Quantum Gravity (LQG). We study the simple model of static black holes: the horizon is made of a given number of identical elementary surfaces and these small surfaces all behaves as a spin-s system accordingly to LQG. The chosen spin-s defines the area unit or area resolution, which the observer uses to probe the space(time) geometry. For s=1/2, we are actually dealing with the qubit model, where the horizon is made of a certain number of qubits. In this context, we compute the black hole entropy and show that the factor in front of the logarithmic correction to the entropy formula is independent of the unit s. We also compute the entanglement between parts of the horizon. We show that these correlations between parts of the horizon are directly responsible for the asymptotic logarithmic corrections. This leads us to speculate on a relation between the evaporation process and the entanglement between a pair of qubits and the rest of the horizon. Finally, we introduce a concept of renormalisation of areas in LQG.Comment: Revtex4, 25 pages, 4 figure

Theory of Parabolic Arcs in Interstellar Scintillation Spectra

Our theory relates the secondary spectrum, the 2D power spectrum of the radio dynamic spectrum, to the scattered pulsar image in a thin scattering screen geometry. Recently discovered parabolic arcs in secondary spectra are generic features for media that scatter radiation at angles much larger than the rms scattering angle. Each point in the secondary spectrum maps particular values of differential arrival-time delay and fringe rate (or differential Doppler frequency) between pairs of components in the scattered image. Arcs correspond to a parabolic relation between these quantities through their common dependence on the angle of arrival of scattered components. Arcs appear even without consideration of the dispersive nature of the plasma. Arcs are more prominent in media with negligible inner scale and with shallow wavenumber spectra, such as the Kolmogorov spectrum, and when the scattered image is elongated along the velocity direction. The arc phenomenon can be used, therefore, to constrain the inner scale and the anisotropy of scattering irregularities for directions to nearby pulsars. Arcs are truncated by finite source size and thus provide sub micro arc sec resolution for probing emission regions in pulsars and compact active galactic nuclei. Multiple arcs sometimes seen signify two or more discrete scattering screens along the propagation path, and small arclets oriented oppositely to the main arc persisting for long durations indicate the occurrence of long-term multiple images from the scattering screen.Comment: 22 pages, 11 figures, submitted to the Astrophysical Journa

Mechanism of age-dependent susceptibility and novel treatment strategy in glutaric acidemia type I

Glutaric acidemia type I (GA-I) is an inherited disorder of lysine and tryptophan metabolism presenting with striatal lesions anatomically and symptomatically similar to Huntington disease. Affected children commonly suffer acute brain injury in the context of a catabolic state associated with nonspecific illness. The mechanisms underlying injury and age-dependent susceptibility have been unknown, and lack of a diagnostic marker heralding brain injury has impeded intervention efforts. Using a mouse model of GA-I, we show that pathologic events began in the neuronal compartment while enhanced lysine accumulation in the immature brain allowed increased glutaric acid production resulting in age-dependent injury. Glutamate and GABA depletion correlated with brain glutaric acid accumulation and could be monitored in vivo by proton nuclear magnetic resonance (1H NMR) spectroscopy as a diagnostic marker. Blocking brain lysine uptake reduced glutaric acid levels and brain injury. These findings provide what we believe are new monitoring and treatment strategies that may translate for use in human GA-I

The theory of heating of the quantum ground state of trapped ions

Using a displacement operator formalism, I analyse the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behaviour, the other long time behaviour are found. The short time behaviour is analyzed both for single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation is considered.Comment: 9 pages, 2 figure

The Initial Conditions of Clustered Star Formation III. The Deuterium Fractionation of the Ophiuchus B2 Core

We present N2D+ 3-2 (IRAM) and H2D+ 1_11 - 1_10 and N2H+ 4-3 (JCMT) maps of the small cluster-forming Ophiuchus B2 core in the nearby Ophiuchus molecular cloud. In conjunction with previously published N2H+ 1-0 observations, the N2D+ data reveal the deuterium fractionation in the high density gas across Oph B2. The average deuterium fractionation R_D = N(N2D+)/N(N2H+) ~ 0.03 over Oph B2, with several small scale R_D peaks and a maximum R_D = 0.1. The mean R_D is consistent with previous results in isolated starless and protostellar cores. The column density distributions of both H2D+ and N2D+ show no correlation with total H2 column density. We find, however, an anticorrelation in deuterium fractionation with proximity to the embedded protostars in Oph B2 to distances >= 0.04 pc. Destruction mechanisms for deuterated molecules require gas temperatures greater than those previously determined through NH3 observations of Oph B2 to proceed. We present temperatures calculated for the dense core gas through the equating of non-thermal line widths for molecules (i.e., N2D+ and H2D+) expected to trace the same core regions, but the observed complex line structures in B2 preclude finding a reasonable result in many locations. This method may, however, work well in isolated cores with less complicated velocity structures. Finally, we use R_D and the H2D+ column density across Oph B2 to set a lower limit on the ionization fraction across the core, finding a mean x_e, lim >= few x 10^{-8}. Our results show that care must be taken when using deuterated species as a probe of the physical conditions of dense gas in star-forming regions.Comment: ApJ accepte

Investigation of Resonant Photoemission in Gd with X-Ray Linear Dichroism

The constructive summing of direct and indirect channels above the absorption threshold of a core level can cause a massive increase in the emission cross section, leading to a phenomenon called resonant photoemission. Using novel magnetic linear dichroism in angular distribution photoelectron spectroscopy experiments and theoretical simulations, we have probed the nature of the resonant photoemission process in Gd metal. It now appears that temporal matching as well as energy matching is a requirement for true resonant photoemission

Nature of Resonant Photoemission in Gd

The phenomenon of resonant photoemission happens when, in addition to a direct photoemission channel, a second indirect channel opens up as the absorption threshold of a core level is crossed. A massive increase in emission cross section can occur, but the nature of the process remains clouded. Using novel magnetic linear dichroism in photoelectron spectroscopy experiments and theoretical calculations, we can now clearly demonstrate that temporal matching of the processes as well as energy matching is a requirement for true resonant photoemission.