1,282 research outputs found
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
Entanglement and alpha entropies for a massive scalar field in two dimensions
We find the analytic expression of the trace of powers of the reduced density
matrix on an interval of length L, for a massive boson field in 1+1 dimensions.
This is given exactly (except for a non universal factor) in terms of a finite
sum of solutions of non linear differential equations of the Painlev\'e V type.
Our method is a generalization of one introduced by Myers and is based on the
explicit calculation of quantities related to the Green function on a plane,
where boundary conditions are imposed on a finite cut. It is shown that the
associated partition function is related to correlators of exponential
operators in the Sine-Gordon model in agreement with a result by Delfino et al.
We also compute the short and long distance leading terms of the entanglement
entropy. We find that the bosonic entropic c-function interpolates between the
Dirac and Majorana fermion ones given in a previous paper. Finally, we study
some universal terms for the entanglement entropy in arbitrary dimensions
which, in the case of free fields, can be expressed in terms of the two
dimensional entropy functions.Comment: 13 pages, 2 figure
Dichroic Masers due to Radiation Anisotropy and the Influence of the Hanle Effect on the Circumstellar SiO Polarization
The theory of the generation and transfer of polarized radiation, mainly
developed for interpreting solar spectropolarimetric observations, allows to
reconsider, in a more rigorous and elegant way, a physical mechanism that has
been suggested some years ago to interpret the high degree of polarization
often observed in astronomical masers. This mechanism, for which the name of
'dichroic maser' is proposed, can operate when a low density molecular cloud is
illuminated by an anisotropic source of radiation (like for instance a nearby
star). Here we investigate completely unsaturated masers and show that
selective stimulated emission processes are capable of producing highly
polarized maser radiation in a non-magnetic environment. The polarization of
the maser radiation is linear and is directed tangentially to a ring
equidistant to the central star. We show that the Hanle effect due to the
presence of a magnetic field can produce a rotation (from the tangential
direction) of the polarization by more that 45 degrees for some selected
combinations of the strength, inclination and azimuth of the magnetic field
vector. However, these very same conditions produce a drastic inhibition of the
maser effect. The rotations of about 90 degrees observed in SiO masers in the
evolved stars TX Cam by Kemball & Diamond (1997) and IRC+10011 by Desmurs et al
(2000) may then be explainedby a local modification of the anisotropy of the
radiation field, being transformed from mainly radial to mainly tangential.Comment: Accepted for publication on Ap
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
Entanglement entropy of two disjoint intervals in conformal field theory
We study the entanglement of two disjoint intervals in the conformal field
theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any
integer n is calculated as the four-point function of a particular type of
twist fields and the final result is expressed in a compact form in terms of
the Riemann-Siegel theta functions. In the decompactification limit we provide
the analytic continuation valid for all model parameters and from this we
extract the entanglement entropy. These predictions are checked against
existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos
corrected and refs adde
On the Magnetic Field Strength of Active Region Filaments
We study the vector magnetic field of a filament observed over a compact
Active Region Neutral Line. Spectropolarimetric data acquired with TIP-II (VTT,
Tenerife, Spain) of the 10830 \AA spectral region provide full Stokes vectors
which were analyzed using three different methods: magnetograph analysis,
Milne-Eddington inversions and PCA-based atomic polarization inversions. The
inferred magnetic field strengths in the filament are of the order of 600 - 700
G by all these three methods. Longitudinal fields are found in the range of 100
- 200 G whereas the transverse components become dominant, with fields as large
as 500 - 600 G. We find strong transverse fields near the Neutral Line also at
photospheric levels. Our analysis indicates that strong (higher than 500 G, but
below kG) transverse magnetic fields are present in Active Region filaments.
This corresponds to the highest field strengths reliably measured in these
structures. The profiles of the Helium 10830 \AA lines observed in this Active
Region filament are dominated by the Zeeman effect.Comment: Accepted for publication in Astronomy and Astrophysics, 9 pages, 4
figure
A human–AI collaboration workflow for archaeological sites detection
This paper illustrates the results obtained by using pre-trained semantic segmentation deep learning models for the detection of archaeological sites within the Mesopotamian floodplains environment. The models were fine-tuned using openly available satellite imagery and vector shapes coming from a large corpus of annotations (i.e., surveyed sites). A randomized test showed that the best model reaches a detection accuracy in the neighborhood of 80%. Integrating domain expertise was crucial to define how to build the dataset and how to evaluate the predictions, since defining if a proposed mask counts as a prediction is very subjective. Furthermore, even an inaccurate prediction can be useful when put into context and interpreted by a trained archaeologist. Coming from these considerations we close the paper with a vision for a Human–AI collaboration workflow. Starting with an annotated dataset that is refined by the human expert we obtain a model whose predictions can either be combined to create a heatmap, to be overlaid on satellite and/or aerial imagery, or alternatively can be vectorized to make further analysis in a GIS software easier and automatic. In turn, the archaeologists can analyze the predictions, organize their onsite surveys, and refine the dataset with new, corrected, annotations
Entanglement entropy and the Berry phase in solid states
The entanglement entropy (von Neumann entropy) has been used to characterize
the complexity of many-body ground states in strongly correlated systems. In
this paper, we try to establish a connection between the lower bound of the von
Neumann entropy and the Berry phase defined for quantum ground states. As an
example, a family of translational invariant lattice free fermion systems with
two bands separated by a finite gap is investigated. We argue that, for one
dimensional (1D) cases, when the Berry phase (Zak's phase) of the occupied band
is equal to and when the ground state respects a
discrete unitary particle-hole symmetry (chiral symmetry), the entanglement
entropy in the thermodynamic limit is at least larger than (per
boundary), i.e., the entanglement entropy that corresponds to a maximally
entangled pair of two qubits. We also discuss this lower bound is related to
vanishing of the expectation value of a certain non-local operator which
creates a kink in 1D systems.Comment: 11 pages, 4 figures, new references adde
Geometric entropy, area, and strong subadditivity
The trace over the degrees of freedom located in a subset of the space
transforms the vacuum state into a density matrix with non zero entropy. This
geometric entropy is believed to be deeply related to the entropy of black
holes. Indeed, previous calculations in the context of quantum field theory,
where the result is actually ultraviolet divergent, have shown that the
geometric entropy is proportional to the area for a very special type of
subsets. In this work we show that the area law follows in general from simple
considerations based on quantum mechanics and relativity. An essential
ingredient of our approach is the strong subadditive property of the quantum
mechanical entropy.Comment: Published versio
Scattering polarization of hydrogen lines from electric-induced atomic alignment
We consider a gas of hydrogen atoms illuminated by a broadband, unpolarized
radiation with zero anisotropy. In the absence of external fields, the atomic
J-levels are thus isotropically populated. While this condition persists in the
presence of a magnetic field, we show instead that electric fields can induce
the alignment of those levels. We also show that this electric alignment cannot
occur in a two-term model of hydrogen (e.g., if only the Ly-alpha transition is
excited), or if the level populations are distributed according to Boltzmann's
law.Comment: 10 pages, 4 figures. Accepted by J.Phys.B: At.Mol.Opt.Phy
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