scholarly journals Reflected entropy for an evaporating black hole

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Tianyi Li ◽  
Jinwei Chu ◽  
Yang Zhou
Keyword(s):  
Black Hole ◽  
Cross Section ◽  
Early Time ◽  
Three Dimensions ◽  
Late Time ◽  
Mixed States ◽  
Correlation Measure ◽  
Extremal Surface ◽  
Brane Model ◽  
The Right

Abstract We study reflected entropy as a mixed state correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and radiation, radiation and radiation, and even black hole and black hole. We compute reflected entropy curves in three different models: 3-side wormhole model, End-of-the-World (EOW) brane model in three dimensions and two-dimensional eternal black hole plus CFT model. For 3-side wormhole model, we find that reflected entropy is dual to island cross section. The reflected entropy between radiation and black hole increases at early time and then decreases to zero, similar to Page curve, but with a later transition time. The reflected entropy between radiation and radiation first increases and then saturates. For the EOW brane model, similar behaviors of reflected entropy are found.We propose a quantum extremal surface for reflected entropy, which we call quantum extremal cross section. In the eternal black hole plus CFT model, we find a generalized formula for reflected entropy with island cross section as its area term by considering the right half as the canonical purification of the left. Interestingly, the reflected entropy curve between the left black hole and the left radiation is nothing but the Page curve. We also find that reflected entropy between the left black hole and the right black hole decreases and goes to zero at late time. The reflected entropy between radiation and radiation increases at early time and saturates at late time.

scholarly journals SHOCK WAVE COLLISIONS IN AdS5: APPROXIMATE NUMERICAL SOLUTIONS

2011 ◽  
Vol 22 (12) ◽  
pp. 1317-1342 ◽  
Author(s):  
BIN WU ◽  
PAUL ROMATSCHKE
Keyword(s):  
Shock Wave ◽  
Black Hole ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Early Time ◽  
Heavy Ion ◽  
Late Time ◽  
Time Behavior ◽  
Ion Collisions ◽  
Bulk System

We numerically study the evolution of a boost-invariant [Formula: see text] SYM medium using AdS/CFT . We consider a toy model for the collision of gravitational shock waves, finding that the energy density first increases, reaches a maximum and then starts to decrease, matching hydrodynamics for late times. For the initial conditions we consider, the hydrodynamic scale governing the late time behavior is to very good approximation determined by the area of the black hole horizon at initial times. Our results provide a toy model for the early time evolution of the bulk system in heavy-ion collisions at RHIC and the LHC.

scholarly journals Evolution of entanglement wedge cross section following a global quench

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Komeil Babaei Velni ◽  
M. Reza Mohammadi Mozaffar ◽  
M.H. Vahidinia
Keyword(s):  
Cross Section ◽  
Linear Growth ◽  
Early Time ◽  
Quadratic Growth ◽  
Late Time ◽  
Zero Temperature ◽  
Information Measures ◽  
Logarithmic Negativity ◽  
Linear Behavior ◽  
Logarithmic Growth

Abstract We study the evolution of entanglement wedge cross section (EWCS) in the Vaidya geometry describing a thin shell of null matter collapsing into the AdS vacuum to form a black brane. In the holographic context, it is proposed that this quantity is dual to different information measures including entanglement of purification, reflected entropy, odd entropy and logarithmic negativity. In 2 + 1 dimensions, we present a combination of numerical and analytic results on the evolution and scaling of EWCS for strip shaped boundary subregions after a thermal quench. In the limit of large subregions, we find that the time evolution of EWCS is characterized by three different scaling regimes: an early time quadratic growth, an intermediate linear growth and a late time saturation. Further, in 3 + 1 dimensions, we examine the scaling behavior by considering thermal and electromagnetic quenches. In the case of a thermal quench, our numerical analysis supply results similar to observations made for the lower dimension. On the other hand, for electromagnetic quenches at zero temperature, an interesting feature is a departure from the linear behavior of the evolution to logarithmic growth.

scholarly journals Entanglement wedge reconstruction and the information paradox

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Geoffrey Penington
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
State Dependence ◽  
Absorbing Boundary Conditions ◽  
Late Time ◽  
Mixed States ◽  
Initial State ◽  
Absorbing Boundary ◽  
The Past

Abstract When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/2πlogSBH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall.By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

NEW RESULTS IN BLACK HOLE PHYSICS

1994 ◽  
Vol 03 (01) ◽  
pp. 317-321
Author(s):  
BERNARD F. WHITING
Keyword(s):  
Black Hole ◽  
Quantum Coherence ◽  
Mechanical Stability ◽  
Black Hole Physics ◽  
Black Hole Entropy ◽  
Late Time ◽  
Mixed States ◽  
University Of Maryland ◽  
Hebrew University ◽  
The Relationship

Brief statements are given on recent results in the following areas: 1) The derivation of a variational (maximum) principle for black hole entropy, and an outline of the physically reasonable properties of the related solution for the density of states in the microcanonical equilibrium ensemble (with Jeffrey Melmed, University of Maine). 2) Analysis of topological contributions to black hole entropy in Lovelock gravity, and the corresponding thermodynamic identity (with Jonathan Z. Simon, University of Maryland). 3) Stability analysis for a shell of matter surrounding a black hole in microcanonical (thermal) equilibrium (with Gerald Horwitz, Hebrew University, Jerusalem)—results from this work can be compared with an earlier analysis of the purely mechanical stability of the shell, and with known properties of both the dynamical and thermal stability for the black hole without a shell. 4) The study of a simple ‘singularity'-free model of gravitational collapse, and an examination of the relationship between the ensuing preservation of quantum coherence and the usual perception that mixed states should be associated with the late time emission of Hawking radiation from a classically formed black hole (with Gerard ’t Hooft and Chris Stephens, University of Utrecht).

scholarly journals The Markov gap for geometric reflected entropy

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Patrick Hayden ◽  
Onkar Parrikar ◽  
Jonathan Sorce
Keyword(s):  
Lower Bound ◽  
Cross Section ◽  
Multipartite Entanglement ◽  
Correlation Measure ◽  
Extremal Surface ◽  
Information Theoretic ◽  
Fixed Area ◽  
Quantum Mutual Information ◽  
Recovery Problem ◽  
Symmetric States

Abstract The reflected entropy SR(A : B) of a density matrix ρAB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N2 gap between SR and I. We provide an information-theoretic interpretation of this gap by observing that SR− I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity SR− I the Markov gap. We then prove that for time-symmetric states in pure AdS3 gravity, the Markov gap is universally lower bounded by log(2)ℓAdS/2GN times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling SR− I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

Propiedades psicométricas de la Escala de Autoritarismo de Derechas en población colombiana

2020 ◽  
Author(s):  
Efrain Garcia-Sanchez ◽  
Nelson Molina Valencia ◽  
Estefanía Buitrago ◽  
Zabdi Sanz ◽  
Valentina Ramírez ◽  
...  
Keyword(s):  
Psychometric Properties ◽  
Empirical Evidence ◽  
Social Dominance ◽  
Three Dimensions ◽  
Social Policies ◽  
The Right

El autoritarismo es un constructo ampliamente estudiado en psicología para investigar comportamientos políticos. Para su medición se suele usar la escala de autoritarismo de derechas (RWA), la cual tiene variaciones en sus propiedades psicométricas según cada contexto. En este artículo traducimos y adaptamos una versión reducida del autoritarismo de derechas al contexto colombiano. En dos estudios (NEstudio1=417;NEstudio2=396), identificamos tres dimensiones: agresión-autoritaria, sumisión-autoritaria y convencionalismo; y encontramos que la RWA estuvo asociada positivamente con: dominancia social, deshumanización del adversario, apoyo al conflicto, patriotismo, sexismo, homofobia y la prohibición de políticas sociales consideradas como liberales (e.g., aborto, matrimonio igualitario, eutanasia). Se aporta evidencia empírica a favor de las propiedades psicométricas de la escala de RWA en el contexto colombiano. Authoritarianism is widely used construct to study political behaviors.For its measurement, researchers usually use the right authoritarianism scale (RWA), which has variations in its psychometric properties according to each context. In this article we translate and adapt a reduced version of RWA to the Colombian context. In two studies (NStudy1=417; NStudy2=396), we identified three dimensions: authoritarian-aggression, authoritarian-submission,and conventionalism. We also found that RWA was positively associated with: social dominance, dehumanization of the adversary, support for conflict, patriotism, sexism, homophobia and the prohibition of social policies considered liberal (e.g., abortion, equal marriage, euthanasia). Empirical evidence is provided in favor of the psychometric properties of the RWA scale in the Colombian context

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

scholarly journals A CBCT Based Three-Dimensional Assessment of Mandibular Posterior Region for Evaluating the Possibility of Bypassing the Inferior Alveolar Nerve While Placing Dental Implants

Diagnostics ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 406 ◽  
Author(s):  
Mohammed G. Sghaireen ◽  
Kumar Chandan Srivastava ◽  
Deepti Shrivastava ◽  
Kiran Kumar Ganji ◽  
Santosh R. Patil ◽  
...  
Keyword(s):  
Nerve Injury ◽  
Age Groups ◽  
Inferior Alveolar Nerve ◽  
Three Dimensions ◽  
High Rate ◽  
Cortical Plate ◽  
Computed Tomography Images ◽  
Group I ◽  
Linear Distance ◽  
The Right

A high rate of nerve injury and related consequences are seen during implant placement in the posterior mandibular arch. An approach has been proposed to avoid nerve injury by dodging the inferior alveolar nerve (IAN) while placing an implant. A prospective study with a total of 240 CBCT (cone beam computed tomography) images of patients with three dentate statuses, namely, edentulous (group I), partially edentulous (group II) and dentate (group III) were included in the study. The nerve path tracing was done on CBCT images with On-demand 3D software. The three dimensions, i.e., the linear distance from the outer buccal cortical plate to the inferior alveolar nerve (BCPN), linear distance from the outer lingual cortical plate to the inferior alveolar nerve (LCPN) and linear distance from the midpoint of the alveolar crest to the inferior alveolar nerve (ACN) were assessed. The data were presented and analyzed between variables using one-way ANOVA and independent t-test in SPSS version 21.LCPN of the right 1st premolar region (p < 0.05) was significantly different among the groups with edentulous subjects recorded with the minimum value (6.50 ± 1.20 mm). Females were found to have significantly (p < 0.05) less available bone (6.03 ± 1.46 mm) on the right side of the mandibular jaw compared to males in edentulous group of patients. On comparing age groups for partially edentulous subjects, LCPN of the right 1st premolar region had significantly (p < 0.05) less available bone (6.03 ± 0.38 mm) in subjects with age ≥54 years. The IAN follows a lingual course in the molar region and later flips to the buccal side in the premolar region. The LCPN dimension in the 1st and 2nd premolar region was found to be more than 6 mm irrespective of age, gender and side of the jaw. Thus, it can be considered as a suitable site for placing implants while bypassing the IAN with CBCT assessment remaining as the mainstay in the pre-surgical phase.

scholarly journals Comparing Glioblastoma Surgery Decisions Between Teams Using Brain Maps of Tumor Locations, Biopsies, and Resections

2019 ◽  
pp. 1-12 ◽  
Author(s):  
Domenique M.J. Müller ◽  
Pierre A.J.T. Robe ◽  
Roelant S. Eijgelaar ◽  
Marnix G. Witte ◽  
Martin Visser ◽  
...  
Keyword(s):  
Tumor Location ◽  
Three Dimensions ◽  
Multidisciplinary Teams ◽  
Surgical Removal ◽  
Treatment Variation ◽  
Probability Maps ◽  
Resected Patient ◽  
The Right ◽  
Referral Bias ◽  
The Brain

Purpose The aim of glioblastoma surgery is to maximize the extent of resection while preserving functional integrity, which depends on the location within the brain. A standard to compare these decisions is lacking. We present a volumetric voxel-wise method for direct comparison between two multidisciplinary teams of glioblastoma surgery decisions throughout the brain. Methods Adults undergoing first-time glioblastoma surgery from 2012 to 2013 performed by two neuro-oncologic teams were included. Patients had had a diagnostic biopsy or resection. Preoperative tumors and postoperative residues were segmented on magnetic resonance imaging in three dimensions and registered to standard brain space. Voxel-wise probability maps of tumor location, biopsy, and resection were constructed for each team to compare patient referral bias, indication variation, and treatment variation. To evaluate the quality of care, subgroups of differentially resected brain regions were analyzed for survival and functional outcome. Results One team included 101 patients, and the other included 174; 91 tumors were biopsied, and 181 were resected. Patient characteristics were largely comparable between teams. Distributions of tumor locations were dissimilar, suggesting referral bias. Distributions of biopsies were similar, suggesting absence of indication variation. Differentially resected regions were identified in the anterior limb of the right internal capsule and the right caudate nucleus, indicating treatment variation. Patients with (n = 12) and without (n = 6) surgical removal in these regions had similar overall survival and similar permanent neurologic deficits. Conclusion Probability maps of tumor location, biopsy, and resection provide additional information that can inform surgical decision making across multidisciplinary teams for patients with glioblastoma.

Sign in / Sign up

Export Citation Format

Share Document