2,205 research outputs found
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
Why and how much the Brouwer's Fixed Point Theorem fails in noncompact setting?
The celebrated Brouwer\u2019s Fixed Point Theorem is dated in 1912. Its extension to compact set setting in Banach spaces due to Schauder appeared in 1930. Immediately it raised the question whether the Theorem can be extended to noncompact setting. The works of Kakutani, Klee, Benyamini and Sterfeld, Sternfeld and Lim solved the qualitative part of the problem. Lack of compactness makes the statement of the theorem false. However, there are some quantitative aspects of the question. The two basic are called minimal displacement problem, and optimal retraction problem. The aim of this article is to present the historical back ground and possibly, up to date state of investigations in this field. A list of open problems with comments will be discussed
AdS/CFT and Strong Subadditivity of Entanglement Entropy
Recently, a holographic computation of the entanglement entropy in conformal
field theories has been proposed via the AdS/CFT correspondence. One of the
most important properties of the entanglement entropy is known as the strong
subadditivity. This requires that the entanglement entropy should be a concave
function with respect to geometric parameters. It is a non-trivial check on the
proposal to see if this property is indeed satisfied by the entropy computed
holographically. In this paper we examine several examples which are defined by
annuli or cusps, and confirm the strong subadditivity via direct calculations.
Furthermore, we conjecture that Wilson loop correlators in strongly coupled
gauge theories satisfy the same relation. We also discuss the relation between
the holographic entanglement entropy and the Bousso bound.Comment: 29 pages, harvmac, 7 figures, references adde
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
Reflexive Cones
Reflexive cones in Banach spaces are cones with weakly compact intersection
with the unit ball. In this paper we study the structure of this class of
cones. We investigate the relations between the notion of reflexive cones and
the properties of their bases. This allows us to prove a characterization of
reflexive cones in term of the absence of a subcone isomorphic to the positive
cone of \ell_{1}. Moreover, the properties of some specific classes of
reflexive cones are investigated. Namely, we consider the reflexive cones such
that the intersection with the unit ball is norm compact, those generated by a
Schauder basis and the reflexive cones regarded as ordering cones in a Banach
spaces. Finally, it is worth to point out that a characterization of reflexive
spaces and also of the Schur spaces by the properties of reflexive cones is
given.Comment: 23 page
On the Weakening of Chromospheric Magnetic Field in Active Regions
Simultaneous measurement of line-of-sight (LOS) magnetic and velocity fields
at the photosphere and chromosphere are presented. Fe I line at
and at are used respectively for deriving the
physical parameters at photospheric and chromospheric heights. The LOS magnetic
field obtained through the center-of-gravity method show a linear relation
between photospheric and chromospheric field for field strengths less than 700
G. But in strong field regions, the LOS magnetic field values derived from
are much weaker than what one gets from the linear relationship
and also from those expected from the extrapolation of the photospheric
magnetic field. We discuss in detail the properties of magnetic field observed
in from the point of view of observed velocity gradients. The
bisector analysis of Stokes profiles show larger velocity
gradients in those places where strong photospheric magnetic fields are
observed. These observations may support the view that the stronger fields
diverge faster with height compared to weaker fields.Comment: accepted for publication in Ap
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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