Non-local properties of multi-particle density matrices

As far as entanglement is concerned, two density matrices of $n$ particles are equivalent if they are on the same orbit of the group of local unitary transformations, $U(d_1)\times...\times U(d_n)$ (where the Hilbert space of particle $r$ has dimension $d_r$). We show that for $n$ greater than or equal to two, the number of independent parameters needed to specify an $n$-particle density matrix up to equivalence is $\Pi_r d_r^2 - \sum_r d_r^2 + n - 1$. For $n$ spin-${1\over 2}$ particles we also show how to characterise generic orbits, both by giving an explicit parametrisation of the orbits and by finding a finite set of polynomial invariants which separate the orbits.Comment: 13 pages RevTe

Normal mere exposure effect with impaired recognition in Alzheimer’s disease.

We investigated the mere exposure effect and the explicit memory in Alzheimer’s disease (AD) patients and elderly control subjects, using unfamiliar faces. During the exposure phase, the subjects estimated the age of briefly flashed faces. The mere exposure effect was examined by presenting pairs of faces (old and new) and asking participants to select the face they liked. The participants were then presented with a forced-choice explicit recognition task. Controls subjects exhibited above-chance preference and recognition scores for old faces. The AD patients also showed the mere exposure effect but no explicit recognition. These results suggest that the processes involved in the mere exposure effect are preserved in AD patients despite their impaired explicit recognition. The results are discussed in terms of Seamon et al.’s proposal (1995) that processes involved in the mere exposure effect are equivalent to those subserving perceptual priming. These processes would depend on extrastriate areas which are relatively preserved in AD patients

On the normality of Higgins commutators

In a semi-abelian context, we study the condition (NH) asking that Higgins commutators of normal subobjects are normal subobjects. We provide examples of categories that do or do not satisfy this property. We focus on the relationship with the "Smith is Huq" condition (SH) and characterise those semi-abelian categories in which both (NH) and (SH) hold in terms of reflection and preservation properties of the change of base functors of the fibration of points.Comment: 15 pages; final published versio

Unstable coronal loops : numerical simulations with predicted observational signatures

We present numerical studies of the nonlinear, resistive magnetohydrodynamic (MHD) evolution of coronal loops. For these simulations we assume that the loops carry no net current, as might be expected if the loop had evolved due to vortex flows. Furthermore the initial equilibrium is taken to be a cylindrical flux tube with line-tied ends. For a given amount of twist in the magnetic field it is well known that once such a loop exceeds a critical length it becomes unstableto ideal MHD instabilities. The early evolution of these instabilities generates large current concentrations. Firstly we show that these current concentrations are consistent with the formation of a current sheet. Magnetic reconnection can only occur in the vicinity of these current concentrations and we therefore couple the resistivity to the local current density. This has the advantage of avoiding resistive diffusion in regions where it should be negligible. We demonstrate the importance of this procedure by comparison with simulations based on a uniform resistivity. From our numerical experiments we are able to estimate some observational signatures for unstable coronal loops. These signatures include: the timescale of the loop brightening; the temperature increase; the energy released and the predicted observable flow speeds. Finally we discuss to what extent these observational signatures are consistent with the properties of transient brightening loops.Comment: 13 pages, 9 figure

Classification of n-qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits. In this paper we show that any state with minimum orbit dimension must be of this form, and furthermore, such states are classified up to local unitary equivalence by the sets of pairs of qubits entangled in singlets.Comment: 15 pages, latex, revision 2, conclusion added, some proofs shortene

Constraining the initial temperature and shear viscosity in a hybrid hydrodynamic model of sNN\sqrt{s_{NN}}=200 GeV Au+Au collisions using pion spectra, elliptic flow, and femtoscopic radii

A new framework for evaluating hydrodynamic models of relativistic heavy ion collisions has been developed. This framework, a Comprehesive Heavy Ion Model Evaluation and Reporting Algorithm (CHIMERA) has been implemented by augmenting UVH 2+1D viscous hydrodynamic model with eccentricity fluctuations, pre-equilibrium flow, and the Ultra-relativistic Quantum Molecular Dynamic (UrQMD) hadronic cascade. A range of initial temperatures and shear viscosity to entropy ratios were evaluated for four initial profiles, $N_{part}$ and $N_{coll}$ scaling with and without pre-equilibrium flow. The model results were compared to pion spectra, elliptic flow, and femtoscopic radii from 200 GeV Au+Au collisions for the 0--20% centrality range.Two sets of initial density profiles, $N_{part}$ scaling with pre-equilibrium flow and $N_{coll}$ scaling without were shown to provide a consistent description of all three measurements.Comment: 21 pages, 32 figures, version 3 includes additional text for clarification, division of figures into more manageable units, and placement of chi-squared values in tables for ease of viewin

Numerical Investigation of Light Scattering off Split-Ring Resonators

Recently, split ring-resonators (SRR's) have been realized experimentally in the near infrared (NIR) and optical regime. In this contribution we numerically investigate light propagation through an array of metallic SRR's in the NIR and optical regime and compare our results to experimental results. We find numerical solutions to the time-harmonic Maxwell's equations by using advanced finite-element-methods (FEM). The geometry of the problem is discretized with unstructured tetrahedral meshes. Higher order, vectorial elements (edge elements) are used as ansatz functions. Transparent boundary conditions and periodic boundary conditions are implemented, which allow to treat light scattering problems off periodic structures. This simulation tool enables us to obtain transmission and reflection spectra of plane waves which are incident onto the SRR array under arbitrary angles of incidence, with arbitrary polarization, and with arbitrary wavelength-dependencies of the permittivity tensor. We compare the computed spectra to experimental results and investigate resonances of the system.Comment: 9 pages, 8 figures (see original publication for images with a better resolution

X-ray bright active galactic nuclei in massive galaxy clusters III: New insights into the triggering mechanisms of cluster AGN

We present the results of a new analysis of the X-ray selected Active Galactic Nuclei (AGN) population in the vicinity of 135 of the most massive galaxy clusters in the redshift range of 0.2 < z < 0.9 observed with Chandra. With a sample of more than 11,000 X-ray point sources, we are able to measure, for the first time, evidence for evolution in the cluster AGN population beyond the expected evolution of field AGN. Our analysis shows that overall number density of cluster AGN scales with the cluster mass as $\sim M_{500}^{-1.2}$. There is no evidence for the overall number density of cluster member X-ray AGN depending on the cluster redshift in a manner different than field AGN, nor there is any evidence that the spatial distribution of cluster AGN (given in units of the cluster overdensity radius r_500) strongly depends on the cluster mass or redshift. The $M^{-1.2 \pm 0.7}$ scaling relation we measure is consistent with theoretical predictions of the galaxy merger rate in clusters, which is expected to scale with the cluster velocity dispersion, $\sigma$, as $\sim \sigma^{-3}$ or $\sim M^{-1}$. This consistency suggests that AGN in clusters may be predominantly triggered by galaxy mergers, a result that is further corroborated by visual inspection of Hubble images for 23 spectroscopically confirmed cluster member AGN in our sample. A merger-driven scenario for the triggering of X-ray AGN is not strongly favored by studies of field galaxies, however, suggesting that different mechanisms may be primarily responsible for the triggering of cluster and field X-ray AGN.Comment: 21 Pages, 8 figures, 5 tables. Submitted to MNRAS. Comments are welcome, and please request Steven Ehlert for higher resolution figure

Probing the extreme realm of AGN feedback in the massive galaxy cluster, RX J1532.9+3021

We present a detailed Chandra, XMM-Newton, VLA and HST analysis of one of the strongest cool core clusters known, RX J1532.9+3021 (z=0.3613). Using new, deep 90 ks Chandra observations, we confirm the presence of a western X-ray cavity or bubble, and report on a newly discovered eastern X-ray cavity. The total mechanical power associated with these AGN-driven outflows is (22+/-9)*10^44 erg/s, and is sufficient to offset the cooling, indicating that AGN feedback still provides a viable solution to the cooling flow problem even in the strongest cool core clusters. Based on the distribution of the optical filaments, as well as a jet-like structure seen in the 325 MHz VLA radio map, we suggest that the cluster harbours older outflows along the north to south direction. The jet of the central AGN is therefore either precessing or sloshing-induced motions have caused the outflows to change directions. There are also hints of an X-ray depression to the north aligned with the 325 MHz jet-like structure, which might represent the highest redshift ghost cavity discovered to date. We further find evidence of a cold front (r=65kpc) that coincides with the outermost edge of the western X-ray cavity and the edge of the radio mini-halo. The common location of the cold front with the edge of the radio mini-halo supports the idea that the latter originates from electrons being reaccelerated due to sloshing induced turbulence. Alternatively, its coexistence with the edge of the X-ray cavity may be due to cool gas being dragged out by the outburst. We confirm that the central AGN is highly sub-Eddington and conclude that a >10^10M_Sun or a rapidly spinning black hole is favoured to explain both the radiative-inefficiency of the AGN and the powerful X-ray cavities.Comment: Accepted for publication to ApJ (minor corrections), 16 pages, 16 figures, 5 tables. Full resolution at http://www.stanford.edu/~juliehl/M1532