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 $B \to VV$ 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 $^{154}$Sm target with various projectiles ranging from $^{12}$C to $^{40}$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 $M\sqrt{\Lambda}$, where $M$ is the central mass and $\Lambda$ is cosmological constant. The low-energy absorption probability, which is in the range of $[0, 0.986701]$, increases monotonically with increase in $\Lambda$. 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 $\Lambda$, as long $\Lambda$ is less than or of the order of $10^4$. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value $27\pi r_g^2/4$.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