449,719 research outputs found
Bulk locality from modular flow
We study the reconstruction of bulk operators in the entanglement wedge in
terms of low energy operators localized in the respective boundary region. To
leading order in , the dual boundary operators are constructed from the
modular flow of single trace operators in the boundary subregion. The
appearance of modular evolved boundary operators can be understood due to the
equality between bulk and boundary modular flows and explicit formulas for bulk
operators can be found with a complete understanding of the action of bulk
modular flow, a difficult but in principle solvable task. We also obtain an
expression when the bulk operator is located on the Ryu-Takayanagi surface
which only depends on the bulk to boundary correlator and does not require the
explicit use of bulk modular flow. This expression generalizes the geodesic
operator/OPE block dictionary to general states and boundary regions.Comment: 36 pages, 2 figure
Master Operators Govern Multifractality in Percolation
Using renormalization group methods we study multifractality in percolation
at the instance of noisy random resistor networks. We introduce the concept of
master operators. The multifractal moments of the current distribution (which
are proportional to the noise cumulants of the
resistance between two sites x and located on the same cluster) are
related to such master operators. The scaling behavior of the multifractal
moments is governed exclusively by the master operators, even though a myriad
of servant operators is involved in the renormalization procedure. We calculate
the family of multifractal exponents for the scaling behavior of the
noise cumulants, ,
where is the correlation length exponent for percolation, to two-loop
order.Comment: 6 page
New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
We construct new, efficient, and accurate high-order finite differencing
operators which satisfy summation by parts. Since these operators are not
uniquely defined, we consider several optimization criteria: minimizing the
bandwidth, the truncation error on the boundary points, the spectral radius, or
a combination of these. We examine in detail a set of operators that are up to
tenth order accurate in the interior, and we surprisingly find that a
combination of these optimizations can improve the operators' spectral radius
and accuracy by orders of magnitude in certain cases. We also construct
high-order dissipation operators that are compatible with these new finite
difference operators and which are semi-definite with respect to the
appropriate summation by parts scalar product. We test the stability and
accuracy of these new difference and dissipation operators by evolving a
three-dimensional scalar wave equation on a spherical domain consisting of
seven blocks, each discretized with a structured grid, and connected through
penalty boundary conditions.Comment: 16 pages, 9 figures. The files with the coefficients for the
derivative and dissipation operators can be accessed by downloading the
source code for the document. The files are located in the "coeffs"
subdirector
The Membership Relation in Fuzzy Operators
Firstly the membership relation in fuzzy operators located outside Zadeh operators be discussed and given. Secondly the membership relation in fuzzy operators located within Zadeh operators be discussed and given
Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on the disk
It is known that the first eigenvalue for Aharonov--Bohm operators with
half-integer circulation in the unit disk is double if the potential's pole is
located at the origin. We prove that in fact it is simple as the pole
Spectrum Sharing for LTE-A Network in TV White Space
Rural areas in the developing countries are predominantly devoid of Internet
access as it is not viable for operators to provide broadband service in these
areas. To solve this problem, we propose a middle mile Long erm Evolution
Advanced (LTE-A) network operating in TV white space to connect villages to an
optical Point of Presence (PoP) located in the vicinity of a rural area. We
study the problem of spectrum sharing for the middle mile networks deployed by
multiple operators. A graph theory based Fairness Constrained Channel
Allocation (FCCA) algorithm is proposed, employing Carrier Aggregation (CA) and
Listen Before Talk (LBT) features of LTE-A. We perform extensive system level
simulations to demonstrate that FCCA not only increases spectral efficiency but
also improves system fairness.Comment: 5 page
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