72,765 research outputs found
Quantum data hiding with spontaneous parameter down-conversion
Here we analyze the practical implication of the existing quantum data hiding
protocol with Bell states produced with optical downconverter. We show that the
uncertainty for the producing of the Bell states with spontaneous parameter
down-conversion should be taken into account, because it will cause serious
trouble to the hider encoding procedure. A set of extended Bell states and a
generalized Bell states analyzer are proposed to describe and analyze the
possible states of two photons distributing in two paths. Then we present a
method to integrate the above uncertainty of Bell states preparation into the
dating hiding procedure, when we encode the secret with the set of extended
Bell states. These modifications greatly simplify the hider's encoding
operations, and thus paves the way for the implementation of quantum data
hiding with present-day quantum optics.Comment: 4 pages, 1 figure, adding some analyse for security proof, to be
appear in Phys. Rev.
Decay and Continuity of Boltzmann Equation in Bounded Domains
Boundaries occur naturally in kinetic equations and boundary effects are
crucial for dynamics of dilute gases governed by the Boltzmann equation. We
develop a mathematical theory to study the time decay and continuity of
Boltzmann solutions for four basic types of boundary conditions: inflow,
bounce-back reflection, specular reflection, and diffuse reflection. We
establish exponential decay in norm for hard potentials for
general classes of smooth domains near an absolute Maxwellian. Moreover, in
convex domains, we also establish continuity for these Boltzmann solutions away
from the grazing set of the velocity at the boundary. Our contribution is based
on a new decay theory and its interplay with delicate
decay analysis for the linearized Boltzmann equation, in the presence of many
repeated interactions with the boundary.Comment: 89 pages
Comparison of Recoil-Induced Resonances (RIR) and Collective Atomic Recoil Laser (CARL)
The theories of recoil-induced resonances (RIR) [J. Guo, P. R. Berman, B.
Dubetsky and G. Grynberg, Phys. Rev. A {\bf 46}, 1426 (1992)] and the
collective atomic recoil laser (CARL) [ R. Bonifacio and L. De Salvo, Nucl.
Instrum. Methods A {\bf 341}, 360 (1994)] are compared. Both theories can be
used to derive expressions for the gain experienced by a probe field
interacting with an ensemble of two-level atoms that are simultaneously driven
by a pump field. It is shown that the RIR and CARL formalisms are equivalent.
Differences between the RIR and CARL arise because the theories are typically
applied for different ranges of the parameters appearing in the theory. The RIR
limit considered in this paper is , while the CARL
limit is , where is the magnitude of the
difference of the wave vectors of the pump and probe fields, is the
width of the atomic momentum distribution and is a recoil
frequency. The probe gain for a probe-pump detuning equal to zero is analyzed
in some detail, in order to understand how the gain arises in a system which,
at first glance, might appear to have vanishing gain. Moreover, it is shown
that the calculations, carried out in perturbation theory have a range of
applicability beyond the recoil problem. Experimental possibilities for
observing CARL are discussed.Comment: 16 pages, 1 figure. Submitted to Physical Review
Radio light curves during the passage of cloud G2 near Sgr A*
We calculate radio light curves produced by the bow shock that is likely to
form in front of the G2 cloud when it penetrates the accretion disk of Sgr A*.
The shock acceleration of the radio-emitting electrons is captured
self-consistently by means of first-principles particle-in-cell simulations. We
show that the radio luminosity is expected to reach maximum in early 2013,
roughly a month after the bow shock crosses the orbit pericenter. We estimate
the peak radio flux at 1.4 GHz to be 1.4 - 22 Jy depending on the assumed orbit
orientation and parameters. We show that the most promising frequencies for
radio observations are in the 0.1<nu<1 GHz range, for which the bow shock
emission will be much stronger than the intrinsic radio flux for all the models
considered.Comment: 15 pages, 10 figures, accepted for publication in MNRA
Effect of monosaccharide sugars on LH-induced differentiation and sugar transport facilitator (SLC2A) expression in sheep theca cells in vitro
Free Rota-Baxter algebras and rooted trees
A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a
linear operator satisfying a relation, called the Rota-Baxter relation, that
generalizes the integration by parts formula. Most of the studies on
Rota-Baxter algebras have been for commutative algebras. Two constructions of
free commutative Rota-Baxter algebras were obtained by Rota and Cartier in the
1970s and a third one by Keigher and one of the authors in the 1990s in terms
of mixable shuffles. Recently, noncommutative Rota-Baxter algebras have
appeared both in physics in connection with the work of Connes and Kreimer on
renormalization in perturbative quantum field theory, and in mathematics
related to the work of Loday and Ronco on dendriform dialgebras and
trialgebras.
This paper uses rooted trees and forests to give explicit constructions of
free noncommutative Rota--Baxter algebras on modules and sets. This highlights
the combinatorial nature of Rota--Baxter algebras and facilitates their further
study. As an application, we obtain the unitarization of Rota-Baxter algebras.Comment: 23 page
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