1,769 research outputs found
Mutual information challenges entropy bounds
We consider some formulations of the entropy bounds at the semiclassical
level. The entropy S(V) localized in a region V is divergent in quantum field
theory (QFT). Instead of it we focus on the mutual information
I(V,W)=S(V)+S(W)-S(V\cup W) between two different non-intersecting sets V and
W. This is a low energy quantity, independent of the regularization scheme. In
addition, the mutual information is bounded above by twice the entropy
corresponding to the sets involved. Calculations of I(V,W) in QFT show that the
entropy in empty space cannot be renormalized to zero, and must be actually
very large. We find that this entropy due to the vacuum fluctuations violates
the FMW bound in Minkowski space. The mutual information also gives a precise,
cutoff independent meaning to the statement that the number of degrees of
freedom increases with the volume in QFT. If the holographic bound holds, this
points to the essential non locality of the physical cutoff. Violations of the
Bousso bound would require conformal theories and large distances. We speculate
that the presence of a small cosmological constant might prevent such a
violation.Comment: 10 pages, 2 figures, minor change
Remarks on the entanglement entropy for disconnected regions
Few facts are known about the entanglement entropy for disconnected regions
in quantum field theory. We study here the property of extensivity of the
mutual information, which holds for free massless fermions in two dimensions.
We uncover the structure of the entropy function in the extensive case, and
find an interesting connection with the renormalization group irreversibility.
The solution is a function on space-time regions which complies with all the
known requirements a relativistic entropy function has to satisfy. We show that
the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields
in dimensions greater than two, and the massive free fields in two dimensions
all fail to be exactly extensive, disproving recent conjectures.Comment: 14 pages, 4 figures, some addition
Removal of Spectro-Polarimetric Fringes by 2D Pattern Recognition
We present a pattern-recognition based approach to the problem of removal of
polarized fringes from spectro-polarimetric data. We demonstrate that 2D
Principal Component Analysis can be trained on a given spectro-polarimetric map
in order to identify and isolate fringe structures from the spectra. This
allows us in principle to reconstruct the data without the fringe component,
providing an effective and clean solution to the problem. The results presented
in this paper point in the direction of revising the way that science and
calibration data should be planned for a typical spectro-polarimetric observing
run.Comment: ApJ, in pres
Positivity, entanglement entropy, and minimal surfaces
The path integral representation for the Renyi entanglement entropies of
integer index n implies these information measures define operator correlation
functions in QFT. We analyze whether the limit , corresponding
to the entanglement entropy, can also be represented in terms of a path
integral with insertions on the region's boundary, at first order in .
This conjecture has been used in the literature in several occasions, and
specially in an attempt to prove the Ryu-Takayanagi holographic entanglement
entropy formula. We show it leads to conditional positivity of the entropy
correlation matrices, which is equivalent to an infinite series of polynomial
inequalities for the entropies in QFT or the areas of minimal surfaces
representing the entanglement entropy in the AdS-CFT context. We check these
inequalities in several examples. No counterexample is found in the few known
exact results for the entanglement entropy in QFT. The inequalities are also
remarkable satisfied for several classes of minimal surfaces but we find
counterexamples corresponding to more complicated geometries. We develop some
analytic tools to test the inequalities, and as a byproduct, we show that
positivity for the correlation functions is a local property when supplemented
with analyticity. We also review general aspects of positivity for large N
theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of
Wilson loops. Conclusions regarding entanglement entropy unchange
A Note on the Radiative and Collisional Branching Ratios in Polarized Radiation Transport with Coherent Scattering
We discuss the implementation of physically meaningful branching ratios
between the CRD and PRD contributions to the emissivity of a polarized
multi-term atom in the presence of both inelastic and elastic collisions. Our
derivation is based on a recent theoretical formulation of partially coherent
scattering, and it relies on a heuristic diagrammatic analysis of the various
radiative and collisional processes to determine the proper form of the
branching ratios. The expression we obtain for the emissivity is
, where and
are the emissivity terms for the redistributed and
partially coherent radiation, respectively, and where "f.s." implies that the
corresponding term must be evaluated assuming a flat-spectrum average of the
incident radiation
Optimizing the computation of overriding
We introduce optimization techniques for reasoning in DLN---a recently
introduced family of nonmonotonic description logics whose characterizing
features appear well-suited to model the applicative examples naturally arising
in biomedical domains and semantic web access control policies. Such
optimizations are validated experimentally on large KBs with more than 30K
axioms. Speedups exceed 1 order of magnitude. For the first time, response
times compatible with real-time reasoning are obtained with nonmonotonic KBs of
this size
Universal terms for the entanglement entropy in 2+1 dimensions
We show that the entanglement entropy and alpha entropies corresponding to
spatial polygonal sets in dimensions contain a term which scales
logarithmically with the cutoff. Its coefficient is a universal quantity
consisting in a sum of contributions from the individual vertices. For a free
scalar field this contribution is given by the trace anomaly in a three
dimensional space with conical singularities located on the boundary of a plane
angular sector. We find its analytic expression as a function of the angle.
This is given in terms of the solution of a set of non linear ordinary
differential equations. For general free fields, we also find the small-angle
limit of the logarithmic coefficient, which is related to the two dimensional
entropic c-functions. The calculation involves a reduction to a two dimensional
problem, and as a byproduct, we obtain the trace of the Green function for a
massive scalar field in a sphere where boundary conditions are specified on a
segment of a great circle. This also gives the exact expression for the
entropies for a scalar field in a two dimensional de Sitter space.Comment: 15 pages, 3 figures, extended version with full calculations, added
reference
Analytic results on the geometric entropy for free fields
The trace of integer powers of the local density matrix corresponding to the
vacuum state reduced to a region V can be formally expressed in terms of a
functional integral on a manifold with conical singularities. Recently, some
progress has been made in explicitly evaluating this type of integrals for free
fields. However, finding the associated geometric entropy remained in general a
difficult task involving an analytic continuation in the conical angle. In this
paper, we obtain this analytic continuation explicitly exploiting a relation
between the functional integral formulas and the Chung-Peschel expressions for
the density matrix in terms of correlators. The result is that the entropy is
given in terms of a functional integral in flat Euclidean space with a cut on V
where a specific boundary condition is imposed. As an example we get the exact
entanglement entropies for massive scalar and Dirac free fields in 1+1
dimensions in terms of the solutions of a non linear differential equation of
the Painleve V type.Comment: 7 pages, minor change
Short-distance regularity of Green's function and UV divergences in entanglement entropy
Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate
space we point out that no matter how regular is short-distance behavior of
Green's function the entanglement entropy in the corresponding quantum field
theory is always UV divergent. In particular, we discuss a recent example by
Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regular Green's function and show
that provided this function arises in a field theory the entanglement entropy
in this theory is UV divergent and calculate the leading divergent term.Comment: LaTeX, 6 page
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