111 research outputs found
An entropic uncertainty principle for positive operator valued measures
Extending a recent result by Frank and Lieb, we show an entropic uncertainty
principle for mixed states in a Hilbert space relatively to pairs of positive
operator valued measures that are independent in some sense. This yields
spatial-spectral uncertainty principles and log-Sobolev inequalities for
invariant operators on homogeneous spaces, which are sharp in the compact case.Comment: 14 pages. v2: a technical assumption removed in main resul
Polarizations in decays B_{u,d}\to VV and possible implications for R-parity violating SUSY
Recently BABAR and Belle have measured anomalous large transverse
polarizations in some pure penguin decays, which might be
inconsistent with the Standard Model expectations. We try to explore its
implications for R-parity violating (RPV) supersymmetry. The QCD factorization
approach is employed for the hadronic dynamics of B decays. We find that it is
possible to have parameter spaces solving the anomaly. Furthermore, we have
derived stringent bounds on relevant RPV couplings from the experimental data,
which is useful for further studies of RPV phenomena.Comment: 26 pages, 12 eps figures. Typos corrected and references added. Final
version to appear in PR
Irreducible modules over finite simple Lie conformal superalgebras of type K
We construct all finite irreducible modules over Lie conformal superalgebras
of type KComment: Accepted for publication in J. Math. Phys
Applicability of the orientation average formula in heavy-ion fusion reactions of deformed nuclei
In heavy-ion fusion reactions involving a well deformed nucleus, one often
assumes that the orientation of the target nucleus does not change during the
reaction. We discuss the accuracy of this procedure by analyzing the excitation
function of the fusion cross section and the fusion barrier distribution in the
reactions of Sm target with various projectiles ranging from C
to Ar. It is shown that the approximation gradually looses its accuracy
with increasing charge product of the projectile and target nuclei because of
the effects of finite excitation energy of the target nucleus. The relevance of
such inaccuracy in analyzing the experimental data is also discussed.Comment: 5 pages and 3 figure
Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes
We study the absorption and scattering of massless scalar waves propagating
in spherically symmetric spacetimes with dynamical cosmological constant both
in low-energy and high-energy zones. In the former low-energy regime, we solve
analytically the Regge-Wheeler wave equation and obtain an analytic absorption
probability expression which varies with , where is the
central mass and is cosmological constant. The low-energy absorption
probability, which is in the range of , increases monotonically
with increase in . In the latter high-energy regime, the scalar
particles adopt their geometric optics limit value. The trajectory equation
with effective potential emerges and the analytic high-energy greybody factor,
which is relevant with the area of classically accessible regime, also
increases monotonically with increase in , as long is less
than or of the order of . In this high-energy case, the null cosmological
constant result reduces to the Schwarzschild value .Comment: 12 pages, 6 figure
Основні тенденції функціонування ринку газу в Україні
Ефективне господарсько-правове регу-
лювання функціонування ринку природного газу в Україні має велике
значення, що підтверджується високим місцем нафтогазового комп-
лексу в національній економіці, а також надзвичайною важливістю
завдання забезпечити енергетичну безпеку України в сучасному
глобалізованому світі.Керівник Стрішенець Олена Миколаївна, д.е.н., професо
Spectral density and Sobolev inequalities for pure and mixed states
We prove some general Sobolev-type and related inequalities for positive
operators A of given ultracontractive spectral decay, without assuming e^{-tA}
is submarkovian. These inequalities hold on functions, or pure states, as
usual, but also on mixed states, or density operators in the quantum mechanical
sense. This provides universal bounds of Faber-Krahn type on domains, that
apply to their whole Dirichlet spectrum distribution, not only the first
eigenvalue. Another application is given to relate the Novikov-Shubin numbers
of coverings of finite simplicial complexes to the vanishing of the torsion of
some l^{p,2}-cohomology
Extended quantum conditional entropy and quantum uncertainty inequalities
Quantum states can be subjected to classical measurements, whose
incompatibility, or uncertainty, can be quantified by a comparison of certain
entropies. There is a long history of such entropy inequalities between
position and momentum. Recently these inequalities have been generalized to the
tensor product of several Hilbert spaces and we show here how their derivations
can be shortened to a few lines and how they can be generalized. All the
recently derived uncertainty relations utilize the strong subadditivity (SSA)
theorem; our contribution relies on directly utilizing the proof technique of
the original derivation of SSA.Comment: 4 page
The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds
The Lie group SU(2) endowed with its canonical subriemannian structure
appears as a three-dimensional model of a positively curved subelliptic space.
The goal of this work is to study the subelliptic heat kernel on it and some
related functional inequalities.Comment: Update: Added section + Correction of typo
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