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Perturbative calculations of entanglement entropy
No full textThis paper is an attempt to extend the recent understanding of the Page curve
for evaporating black holes to more general systems coupled to a heat bath.
Although calculating the von Neumann entropy by the replica trick is usually a
challenge, we have identified two solvable cases. For the initial section of
the Page curve, we sum up the perturbation series in the system-bath coupling
; the most interesting contribution is of order , where is the
number of replicas. For the saturated regime, we consider the effect of an
external impulse on the entropy at a later time and relate it to OTOCs. A
significant simplification occurs in the maximal chaos case such that the
effect may be interpreted in terms of an intermediate object, analogous to the
branching surface of a replica wormhole.Comment: 17 pages, 7 figures, fixing an error in section 3.5 has lead to a
much simpler result. An alternative, shorter derivation is given. (new
contributions by a new author, Pengfei Zhang.
Black Holes and Entanglement Entropy
Get PDFWe study the deformation of the thermofield-double (TFD) under evolution by a double-traced operator by computing its entanglement entropy. After saturation, the entanglement change leads to the temperature change. In Jackiw-Teitelboim gravity, the new temperature can be computed independently from two-point function by considering the Schwarzian modes. We will also derive the entanglement entropy from the Casimir associated with the SL(2,R) symmetry. From AdS/CFT correspondence, where TFD is dual to a two-sided black hole, such deformations correspond to the coherent shrinking or expansion of the black hole.
Next, we compute the entanglement entropy after coupling a system to the bath perturbatively as a function of κ, the system-bath coupling. At very early times where the entanglement entropy is a logarithmic function of time, the leading contribution is due to the terms of order 2s in the coupling where s is the number of replicas. In the middle time, the entanglement goes linear as a function of time. Assuming saturation at a later time, we will study the effect of an external perturbation to the entropy at an early time where it is related to the OTOCs. A major simplification appears when the system saturates the chaos bound.</p
On boundary degrees of freedom in three dimensional Anti-de Sitter spacetime and thermofield-double
Get PDFIn this article, we will study the Gibbons-Hawking-York (GHY) action over a
co-dimension one hypersurface, called the ``physical boundary,'' close to the
boundary of AdS. For that, we take a coordinate system that consists of two
times, one is associated with evolution on the boundary, and the second is
associated with evolution into the bulk. The resulting action is divergent and
needs regularization. We consider two particular schemes. In the first scheme,
we will add the Einstein-Hilbert on-shell action as the counter-term, which,
while cancels the divergent part, adds the contribution of deep in the bulk,
such as an existing horizon. The resulting action includes the Liouville
action, which describes the curvature of the physical boundary. In the second
scheme, however, we prescribe a natural regularization for GHY action without
adding any counter-term. The resulting action will include two copies of
Schwarzian actions associated with the left and right-moving reparametrization
modes. At finite temperature, these modes live on two disjoint circles. We will
show that these are the thermofield-double's effective degrees of freedom.
While the first scheme is more common in practice, the second scheme may be
more convenient for Susskind-'t Hooft proposal for holography.Comment: 42 pages, 6 figure
Disentangling the Thermofield-double state
Get PDFIn this note we will study the evolution of the thermofield-double state under a quantum quench made by double traced operators in the context of SYK model. We will compute the entanglement entropy of the resulting state to second order in the coupling using the replica method. The entanglement entropy will increase (decrease) depending on the sign of the coupling. We will also compute the two point function to leading order. The system will thermalize again after a time of order t ∼ β/2pΔ with a new temperature, where p and Δ are the number of left and right Majorana fermions in the interaction hamiltonian and the scaling dimension of the Majorana fermions, respectively. From bulk point of view the decrease (increase) in entanglement entropy corresponds to the shrinking (expansion) of the black hole's event horizon
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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