3,462 research outputs found
Entropy inequalities from reflection positivity
We investigate the question of whether the entropy and the Renyi entropies of
the vacuum state reduced to a region of the space can be represented in terms
of correlators in quantum field theory. In this case, the positivity relations
for the correlators are mapped into inequalities for the entropies. We write
them using a real time version of reflection positivity, which can be
generalized to general quantum systems. Using this generalization we can prove
an infinite sequence of inequalities which are obeyed by the Renyi entropies of
integer index. There is one independent inequality involving any number of
different subsystems. In quantum field theory the inequalities acquire a simple
geometrical form and are consistent with the integer index Renyi entropies
being given by vacuum expectation values of twisting operators in the Euclidean
formulation. Several possible generalizations and specific examples are
analyzed.Comment: Significantly enlarged and corrected version. Counterexamples found
for the most general form of the inequalities. V3: minor change
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
Multi-line Stokes inversion for prominence magnetic-field diagnostics
We present test results on the simultaneous inversion of the Stokes profiles
of the He I lines at 587.6 nm (D_3) and 1083.0 nm in prominences (90-deg
scattering). We created datasets of synthetic Stokes profiles for the case of
quiescent prominences (B<200 G), assuming a conservative value of 10^-3 of the
peak intensity for the polarimetric sensitivity of the simulated observations.
In this work, we focus on the error analysis for the inference of the magnetic
field vector, under the usual assumption that the prominence can be assimilated
to a slab of finite optical thickness with uniform magnetic and thermodynamic
properties. We find that the simultaneous inversion of the two lines
significantly reduces the errors on the inference of the magnetic field vector,
with respect to the case of single-line inversion. These results provide a
solid justification for current and future instrumental efforts with multi-line
capabilities for the observations of solar prominences and filaments.Comment: 14 pages, 5 figures, 1 tabl
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
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
Space and Time pattern of mid-velocity IMF emission in peripheral heavy-ion collisions at Fermi energies
The emission pattern in the V_perp - V_par plane of Intermediate Mass
Fragments with Z=3-7 (IMF) has been studied in the collision 116Sn + 93Nb at
29.5 AMeV as a function of the Total Kinetic Energy Loss of the reaction. This
pattern shows that for peripheral reactions most of IMF's are emitted at
mid-velocity. Coulomb trajectory calculations demonstrate that these IMF's are
produced in the early stages of the reaction and shed light on geometrical
details of these emissions, suggesting that the IMF's originate both from the
neck and the surface of the interacting nuclei.Comment: 4 pages, 3 figures, RevTex 3.1, submitted to Phys. Rev. Letter
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
Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories
This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability
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