Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarifie

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N {\em strongly correlated} random variables for all values of N (and not just for large N).Comment: 13 pages, 2 figures included; typos corrected; to appear in J. Stat. Phy

The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram

One central challenge in high-$T_c$ superconductivity (SC) is to derive a detailed understanding for the specific role of the $Cu$-$d_{x^2-y^2}$ and $O$-$p_{x,y}$ orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-$T_c$ cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from "high-energy" excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are "universal". On the other hand, we expect the differences - and thus, the material dependence to show up in the "non-universal" finite-T phase diagram ($T_c$-values).Comment: 17 pages, 9 figure

Adherence to a MIND-Like Dietary Pattern, Long-Term Exposure to Fine Particulate Matter Air Pollution, and MRI-Based Measures of Brain Volume: The Women’s Health Initiative Memory Study-MRI

BACKGROUND: Previous studies suggest that certain dietary patterns and constituents may be beneficial to brain health. Airborne exposures to fine particulate matter [particulate matter with aerodynamic diameter ≤2.5 μm (PM2.5)] are neurotoxic, but the combined effects of dietary patterns and PM2.5 have not been investigated. OBJECTIVES: We examined whether previously reported association between PM2.5 exposure and lower white matter volume (WMV) differed between women whose usual diet during the last 3 months before baseline was more or less consistent with a Mediterranean-DASH Intervention for Neurodegenerative Delay (MIND)-like diet, a dietary pattern that may slow neurodegenerative changes. METHODS: This study included 1,302 U.S. women who were 65-79 y old and free of dementia in the period 1996-1998 (baseline). In the period 2005-2006, structural brain magnetic resonance imaging (MRI) scans were performed to estimate normal-appearing brain volumes (excluding areas with evidence of small vessel ischemic disease). Baseline MIND diet scores were derived from a food frequency questionnaire. Three-year average PM2.5 exposure prior to MRI was estimated using geocoded participant addresses and a spatiotemporal model. RESULTS: Average total and temporal lobe WMVs were 0:74 cm3 [95% confidence interval (CI): 0.001, 1.48) and 0:19 cm3 (95% CI: 0.002, 0.37) higher, respectively, with each 0.5-point increase in the MIND score and were 4:16 cm3 (95% CI: -6:99, -1:33) and 1:46 cm3 (95% CI: -2:16, -0:76) lower, respectively, with each interquartile range (IQR) (IQR = 3:22 μg/m3) increase in PM2.5. The inverse association between PM2.5 per IQR and WMV was stronger (p-interaction <0:001) among women with MIND scores below the median (for total WMV, -12:47 cm3; 95% CI: −17:17, −7:78), but absent in women with scores above the median (0:16 cm3; 95% CI: −3:41, 3.72), with similar patterns for WMV in the frontal, parietal, and temporal lobes. For total cerebral and hippocampus brain volumes or WMV in the corpus callosum, the associations with PM2.5 were not significantly different for women with high MIND scores and women with low MIND scores

Cognitive Function and Changes in Cognitive Function as Predictors of Incident Cardiovascular Disease: The Women's Health Initiative Memory Study

Background Cognitive impairment and decline may signal the increased risk of incident cardiovascular disease (CVD). We examined associations of global cognitive function, as measured by the Modified Mini-Mental State Examination (3MS) and changes in 3MS over time, with incident CVD, individual CVD outcomes, CVD death, and all-cause mortality. Methods A total of 5,596 women (≥ 60) from the Women's Health Initiative Memory Study free of CVD at baseline were followed for an average of 7.1 years. The 3MS was measured at baseline and annually thereafter. Cox proportional hazards regressions were used to model associations between baseline 3MS and changes in 3MS and time to events. Results In the fully-adjusted models for every 5-point lower baseline 3MS score, the risk was 12% greater for incident CVD, 37% for HF, 35% for CVD death, and 24% for all-cause mortality. No significant relationships were found for coronary heart disease (CHD), angina, stroke/transient ischemic attack (TIA), or coronary revascularization. When change in 3MS was added as a time-varying covariate in the fully-adjusted models, for every 1-point/year greater decline in 3MS, the risk was 4% greater for incident CVD, 10% for CHD, 9% for Stroke/TIA, 17% for CVD death, and 13% for all-cause mortality. Conclusions In older women free of prevalent CVD at baseline, lower baseline global cognitive function or decline in global cognitive function over time, increased risk of incident CVD, CVD death, and all-cause mortality

B vitamin intakes modify the association between particulate air pollutants and incidence of all-cause dementia: Findings from the Women's Health Initiative Memory Study

Introduction: Particulate air pollutants may induce neurotoxicity by increasing homocysteine levels, which can be lowered by high B vitamin intakes. Therefore, we examined whether intakes of three B vitamins (folate, B12, and B6) modified the association between PM2.5 exposure and incidence of all-cause dementia. Methods: This study included 7183 women aged 65 to 80 years at baseline. B vitamin intakes from diet and supplements were estimated by food frequency questionnaires at baseline. The 3-year average PM2.5 exposure was estimated using a spatiotemporal model. Results: During a mean follow-up of 9 years, 342 participants developed all-cause dementia. We found that residing in locations with PM2.5 exposure above the regulatory standard (12 μg/m3) was associated with a higher risk of dementia only among participants with lower intakes of these B vitamins. Discussion: This is the first study suggesting that the putative neurotoxicity of PM2.5 exposure may be attenuated by high B vitamin intakes

Erythrocyte omega-3 index, ambient fine particle exposure, and brain aging

OBJECTIVE: To examine whether long-chain omega-3 polyunsaturated fatty acid (LCn3PUFA) levels modify the potential neurotoxic effects of particle matter with diameters <2.5 µm (PM2.5) exposure on normal-appearing brain volumes among dementia-free elderly women. METHODS: A total of 1,315 women (age 65-80 years) free of dementia were enrolled in an observational study between 1996 and 1999 and underwent structural brain MRI in 2005 to 2006. According to prospectively collected and geocoded participant addresses, we used a spatiotemporal model to estimate the 3-year average PM2.5 exposure before the MRI. We examined the joint associations of baseline LCn3PUFAs in red blood cells (RBCs) and PM2.5 exposure with brain volumes in generalized linear models. RESULTS: After adjustment for potential confounders, participants with higher levels of RBC LCn3PUFA had significantly greater volumes of white matter and hippocampus. For each interquartile increment (2.02%) in omega-3 index, the average volume was 5.03 cm3 (p < 0.01) greater in the white matter and 0.08 cm3 (p = 0.03) greater in the hippocampus. The associations with RBC docosahexaenoic acid and eicosapentaenoic acid levels were similar. Higher LCn3PUFA attenuated the inverse associations between PM2.5 exposure and white matter volumes in the total brain and multimodal association areas (frontal, parietal, and temporal; all p for interaction <0.05), while the associations with other brain regions were not modified. Consistent results were found for dietary intakes of LCn3PUFAs and nonfried fish. CONCLUSIONS: Findings from this prospective cohort study among elderly women suggest that the benefits of LCn3PUFAs on brain aging may include the protection against potential adverse effects of air pollution on white matter volumes

Contributions of the Women's Health Initiative to Cardiovascular Research: JACC State-of-the-Art Review

The WHI (Women's Health Initiative) enrolled 161,808 racially and ethnically diverse postmenopausal women, ages 50-79 years, from 1993 to 1998 at 40 clinical centers across the United States. In its clinical trial component, WHI evaluated 3 randomized interventions (menopausal hormone therapy; diet modification; and calcium/vitamin D supplementation) for the primary prevention of major chronic diseases, including cardiovascular disease, in older women. In the WHI observational study, numerous clinical, behavioral, and social factors have been evaluated as predictors of incident chronic disease and mortality. Although the original interventions have been completed, the WHI data and biomarker resources continue to be leveraged and expanded through ancillary studies to yield novel insights regarding cardiovascular disease prevention and healthy aging in women

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02