6,430 research outputs found
Localized shocks
We study products of precursors of spatially local operators,
, where .
Using chaotic spin-chain numerics and gauge/gravity duality, we show that a
single precursor fills a spatial region that grows linearly in . In a
lattice system, products of such operators can be represented using tensor
networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges
supported by localized shock waves. We find a geometrical correspondence
between these two descriptions, generalizing earlier work in the spatially
homogeneous case.Comment: 23 pages plus appendices, 12 figures. v2: minor error in Appendix B
corrected. v3: figure added to the introduction comparing the butterfly
effect cone with the standard light con
The development of computer science oriented towards the citizen
The concept of informational application oriented to the citizen is defined. The quality characteristics for the informational applications developed under the conditions of computer science oriented towards the citizen are settled and the structure of the development cycle for these applications is presented. The conditions of existence for applications oriented towards the citizen are defined. Strategies on medium and long term are structured.distributed applications, metric units, orientation towards the citizen, strategies.
Connections between collinear and transverse-momentum-dependent polarized observables within the Collins-Soper-Sterman formalism
We extend the improved Collins-Soper-Sterman (iCSS) construction
recently presented in~\cite{Collins:2016hqq} to the case of polarized
observables, where we focus in particular on the Sivers effect in
semi-inclusive deep-inelastic scattering. We further show how one recovers the
expected leading-order collinear twist-3 result from a (weighted)
-integral of the differential cross section. We are also able to
demonstrate the validity of the well-known relation between the (TMD) Sivers
function and the (collinear twist-3) Qiu-Sterman function within the iCSS
framework. This relation allows for their interpretation as functions yielding
the average transverse momentum of unpolarized quarks in a transversely
polarized spin- target. We further outline how this study can be
generalized to other polarized quantities.Comment: 14 pages, Version to be published in PL
The Power of Strong Fourier Sampling: Quantum Algorithms for Affine Groups and Hidden Shifts
Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a hidden subgroup problem, in which an unknown subgroup of a group must be determined from a quantum state over that is uniformly supported on a left coset of . These hidden subgroup problems are typically solved by Fourier sampling: the quantum Fourier transform of is computed and measured. When the underlying group is nonabelian, two important variants of the Fourier sampling paradigm have been identified: the weak standard method, where only representation names are measured, and the strong standard method, where full measurement (i.e., the row and column of the representation, in a suitably chosen basis, as well as its name) occurs. It has remained open whether the strong standard method is indeed stronger, that is, whether there are hidden subgroups that can be reconstructed via the strong method but not by the weak, or any other known, method. In this article, we settle this question in the affirmative. We show that hidden subgroups of the -hedral groups, i.e., semidirect products , where , and in particular the affine groups , can be information-theoretically reconstructed using the strong standard method. Moreover, if , these subgroups can be fully reconstructed with a polynomial amount of quantum and classical computation. We compare our algorithms to two weaker methods that have been discussed in the literature—the “forgetful” abelian method, and measurement in a random basis—and show that both of these are weaker than the strong standard method. Thus, at least for some families of groups, it is crucial to use the full power of representation theory and nonabelian Fourier analysis, namely, to measure the high-dimensional representations in an adapted basis that respects the group's subgroup structure. We apply our algorithm for the hidden subgroup problem to new families of cryptographically motivated hidden shift problems, generalizing the work of van Dam, Hallgren, and Ip on shifts of multiplicative characters. Finally, we close by proving a simple closure property for the class of groups over which the hidden subgroup problem can be solved efficiently
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