2,238 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
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
Simulation of subseismic joint and fault networks using a heuristic mechanical model
Flow simulations of fractured and faulted reservoirs require representation of subseismic structures about which subsurface data are limited. We describe a method for simulating fracture growth that is mechanically based but heuristic, allowing for realistic modelling of fracture networks with reasonable run times. The method takes a triangulated meshed surface as input, together with an initial stress field. Fractures initiate and grow based on the stress field, and the growing fractures relieve the stress in the mesh. We show that a wide range of bedding-plane joint networks can be modelled simply by varying the distribution and anisotropy of the initial stress field. The results are in good qualitative agreement with natural joint patterns. We then apply the method to a set of parallel veins and demonstrate how the variations in thickness of the veins can be represented. Lastly, we apply the method to the simulation of normal fault patterns on salt domes. We derive the stress field on the bedding surface using the horizon curvature. The modelled fault network shows both radial and concentric faults. The new method provides an effective means of modelling joint and fault networks that can be imported to the flow simulator
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
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
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
The Hydromechanical Interplay in the Simplified Three-Dimensional Limit Equilibrium Analyses of Unsaturated Slope Stability
This paper presents a three-dimensional slope stability limit equilibrium solution for translational planar failure modes. The proposed solution uses Bishop's average skeleton stress combined with the Mohr-Coulomb failure criterion to describe soil strength evolution under unsaturated conditions while its formulation ensures a natural and smooth transition from the unsaturated to the saturated regime and vice versa. The proposed analytical solution is evaluated by comparing its predictions with the results of the Ruedlingen slope failure experiment. The comparison suggests that, despite its relative simplicity, the analytical solution can capture the experimentally observed behaviour well and highlights the importance of considering lateral resistance together with a realistic interplay between mechanical parameters (cohesion) and hydraulic (pore water pressure) conditions
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