Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems

We seek to derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the partial transposes (PT's) of the associated 4 x 4 density matrices). But the full implementation of the test--requiring that the determinant of the PT be nonnegative for separability to hold--appears to be, at least presently, computationally intractable. So, we have previously implemented--using the auxiliary concept of a diagonal-entry-parameterized separability function (DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal minors of the PT. This yielded an exact upper bound on the separability probability of 1024/{135 pi^2} =0.76854$. Here, we piece together (reflection-symmetric) results obtained by requiring that each of the four 3 x 3 principal minors of the PT, in turn, be nonnegative, giving an improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a still further improved upper bound of 1129/2100 = 0.537619 can be found by similarly piecing together the (reflection-symmetric) results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors. In deriving our improved upper bounds, we rely repeatedly upon the use of certain integrals over cubes that arise. Finally, we apply an independence assumption to a pair of DESF's that comes close to reproducing our numerical estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the end are correcte

Gravitational Loss-Cone Instability in Stellar Systems with Retrograde Orbit Precession

We study spherical and disk clusters in a near-Keplerian potential of galactic centers or massive black holes. In such a potential orbit precession is commonly retrograde, i.e. direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly radial orbits. We show that if there is a loss cone at low angular momentum (e.g., due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics $l \ge 3$. If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independently of azimuthal number $m$. The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum. The analysis is based on simple characteristic equations describing small perturbations in a disk or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analyzing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose-Nyquist criterion for disk and spherical gravitational systems.Comment: Accepted to Monthly Notices of the Royal Astronomical Society; typos adde

The Saw Properties Of Sputtered Sio2 On X-112°Y Litao3

The surface acoustic wave (SAW) propagation properties on the X-cut plate, 112°Y rotated, lithium tantalate (LiTaO3) substrate with and without sputtered SiO2 film layers have been investigated using interdigital transducer electrode structures. Thicknesses of SiO2 of 500 nm and 1000 nm were sputter deposited on the X-112°Y LiTaO3 substrates. A series array of aluminum electrode patterns deposited on the film facilitated the excitation of a wide frequency band of harmonic waves up to 2.0 GHz, and permitted delineation of SAW velocity and propagation loss characteristics for several values of film-thickness to acoustic-wavelength (t/λ) ratio. A resonator pattern at the substrate/film interface, permitted the capacitance ratio (Cm/Co), related to coupling factor, and the temperature coefficient of frequency (TCF) to be measured. A high velocity pseudo-SAW (HVPSAW) mode was observed with a velocity near 6300 m/s

Novel Multi-Channel Saw Tool For The Analysis Of Gas-Phase Adsorption

By considering the 6 most popular planes of quartz and LiNbO3, a multi-channel SAW analytical tool for sensing is optimized. The best anisotropy conditions for the SAW velocity, elastic displacement, electric coupling, and temperature sensitivity are found to be on the ST-plane of the former and 128°Y-rotated plane of the latter with orientation of the channels at 0°, -33°, +47° and θ = 0°, 46°, 80°, 115° off x-axis respectively. Based on the optimized orientations, two novel prototypes were fabricated using photomasks integrating all the channels on a single plate. The anisotropy of different channels of the tools was tested for uncoated and PVA coated substrates, both for humid air, as the example. The difference in SAW responses and in the calibration curves of the channels was found to be sufficient to make an appropriate analysis of gas-phase adsorption. The largest number of channels on a substrate was found to be 5

On Bounds for Diffusion, Discrepancy and Fill Distance Metrics

Criteria for optimally discretizing measurable sets in Euclidean space is a difficult and old problem which relates directly to the problem of good numerical integration rules or finding points of low discrepancy. On the other hand, learning meaningful descriptions of a finite number of given points in a measure space is an exploding area of research with applications as diverse as dimension reduction, data analysis, computer vision, critical infrastructure, complex networks, clustering, imaging neural and sensor networks, wireless communications, financial marketing and dynamic programming. The purpose of this paper is to show that a general notion of extremal energy as defined and studied recently by Damelin, Hickernell and Zeng on measurable sets X in Euclidean space, defines a diffusion metric on X which is equivalent to a discrepancy on X and at the same time bounds the fill distance on X for suitable measures with discrete support. The diffusion metric is used to learn via normalized graph Laplacian dimension reduction and the discepancy is used to discretize. Dedicated to Alexander Gorban, Andrei Zinovyev and their co-organisers for the wonderful international workshop on large data sets held at the University of Leicester in August 2006

On the Steady State of an Age-Dependent Model for Malaria

This chapter discusses some basic analysis of the steady state equations of an age-dependent model of malaria, suggested by Klaus Dietz in cooperation with others at the World Health Organization. The model considers population density of the sporozoite (asexual) malarial parasite in a host; the death rate of the sporozoites; and the population density of the gametocyte (sexual) malarial parasite in a host. The sporozoite is involved directly in the effect of the disease on the host but not in the transfer of disease, while the gametocyte has little symptomatic effect but is the key to the spread of the disease via the mosquito. The chapter describes different assumptions that are incorporated in the model