Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.

On the mixing property for a class of states of relativistic quantum fields

Let omega be a factor state on the quasilocal algebra A of observables generated by a relativistic quantum field, which, in addition, satisfies certain regularity conditions [satisfied by ground states and the recently constructed thermal states of the P(phi)(2) theory]. We prove that there exist space- and time-translation invariant states, some of which are arbitrarily close to omega in the weak * topology, for which the time evolution is weakly asymptotically Abelian. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3372623]

Position-dependent noncommutativity in quantum mechanics

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [(x) over cap (i), (x) over cap (j)] = omega(ij) ((x) over cap), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obeys the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativity.

KINETICS VERSUS HYDRODYNAMICS: GENERALIZATION OF LANDAU/COOPER-FRYE PRESCRIPTION FOR FREEZE-OUT

The problem of spectra formation in hydrodynamic approach to A + A collisions is considered within the Boltzmann equations. It is shown analytically and illustrated by numerical calculations that the particle momentum spectra can be presented in the Cooper-R-ye form despite freeze-out is not sharp and has the finite temporal width. The latter is equal to the inverse of the particle collision rate at points (t(sigma) (r, p), r) of the maximal emission at a fixed momentum p. The set of these points forms the hypersurfaces t(sigma)(r,p) which strongly depend on the values of p and typically do not enclose completely the initially dense matter. This is an important difference from the standard Cooper-Frye prescription (CFp), with a common freeze-out hypersurface for all p, that affects significantly the predicted spectra. Also, the well known problem of CFp as for negative contributions to the spectra from non-space-like parts of the freeze-out hypersurface is naturally eliminated in this improved prescription.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Longitudinal double-spin asymmetry and cross section for inclusive neutral pion production at midrapidity in polarized proton collisions at s=200 GeV

We report a measurement of the longitudinal double-spin asymmetry A(LL) and the differential cross section for inclusive pi(0) production at midrapidity in polarized proton collisions at s=200 GeV. The cross section was measured over a transverse momentum range of 1 < p(T)< 17 GeV/c and found to be in good agreement with a next-to-leading order perturbative QCD calculation. The longitudinal double-spin asymmetry was measured in the range of 3.7 < p(T)< 11 GeV/c and excludes a maximal positive gluon polarization in the proton. The mean transverse momentum fraction of pi(0)'s in their parent jets was found to be around 0.7 for electromagnetically triggered events.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Effects of Infrared-LED Illumination Applied During High-Intensity Treadmill Training in Postmenopausal Women

Background data: Technology and physical exercise can enhance physical performance during aging. Objective: The purpose of this study was to investigate the effects of infrared-light-emitting diode (LED) illumination (850 nm) applied during treadmill training. Materials and methods: Twenty postmenopausal women participated in this study. They were randomly divided into two groups. The LED group performed treadmill training associated with infrared-LED illumination (n = 10) and the control group performed only treadmill training (n = 10). The training was performed during 3 months, twice a week during 30 min at intensities between 85 and 90% of maximal heart rate. The irradiation parameters were 31 mW/cm(2), treatment time 30 min, 14,400 J of total energy and 55.8 J/cm(2) of fluence. Physiological, biomechanical, and body composition parameters were measured at the baseline and after 3 months. Results: Both groups improved the time of tolerance limit (Tlim) (p < 0.05) during submaximal constant-speed testing. The peak torque did not differ between groups. However, the results showed significantly higher values of power [from 56 +/- 10 to 73 +/- 8W (p = 0.002)] and total work [from 1,537 +/- 295 to 1,760 +/- 262 J (p = 0.006)] for the LED group when compared to the control group [power: from 58 +/- 14 to 60 +/- 15W (p >= 0.05) and total work: from 1,504 +/- 404 to 1,622 +/- 418 J (p >= 0.05)]. The fatigue significantly increased for the control group [from 51 +/- 6 to 58 +/- 5 % (p = 0.04)], but not for the LED group [from 60 +/- 10 to 60 +/- 4 % (p >= 0.05)]. No significant differences in body composition were observed for either group. Conclusions: Infrared-LED illumination associated with treadmill training can improve muscle power and delay leg fatigue in postmenopausal women.

Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

A Morphological and Histological Characterization of Bisexual and Male Flower Types in Pomegranate

Pomegranate [Punica granatum (Punicaceae)] is characterized by having two types of flowers on the same tree: hermaphroditic bisexual flowers and functionally male flowers. This condition, defined as functional andromonoecy, can result in decreased yields resulting from the inability of male flowers to set fruit. Morphological and histological analyses of bisexual and male flowers were conducted using light and scanning electron microscopy (SEM) to characterize the different flower types observed in pomegranate plants and to better understand their developmental differences. Bisexual flowers had a discoid stigma covered with copious exudate, elongated stigmatic papillae, a single elongate style, and numerous stamens inserted on the inner wall of the calyx tube. Using fluorescence staining, high numbers of pollen tubes were observed growing through a central stylar canal. Ovules were numerous, elliptical, and anatropous. In contrast, male flowers had reduced female parts and exhibited shortened pistils of variable heights. Stigmatic papillae of male flowers had little exudate yet supported pollen germination. However, pollen tubes were rarely observed in styles. Ovules in male flowers were rudimentary and exhibited various stages of degeneration. Pollen from both types of flowers was of similar size, approximate to 20 mu m, and exhibited similar percent germination using in vitro germination assays. Pollen germination was strongly influenced by temperature. Maximal germination (greater than 74%) was obtained at 25 and 35 degrees C; pollen germination was significantly lower at 15 degrees C (58%) and 5 degrees C (10%).

Sequential injections as an alternative to gradient exploitation for implementing differential kinetic analysis in a flow injection system

A novel flow-based strategy for implementing simultaneous determinations of different chemical species reacting with the same reagent(s) at different rates is proposed and applied to the spectrophotometric catalytic determination of iron and vanadium in Fe-V alloys. The method relies on the influence of Fe(II) and V(IV) on the rate of the iodide oxidation by Cr(VI) under acidic conditions, the Jones reducing agent is then needed Three different plugs of the sample are sequentially inserted into an acidic KI reagent carrier stream, and a confluent Cr(VI) solution is added downstream Overlap between the inserted plugs leads to a complex sample zone with several regions of maximal and minimal absorbance values. Measurements performed on these regions reveal the different degrees of reaction development and tend to be more precise Data are treated by multivariate calibration involving the PLS algorithm The proposed system is very simple and rugged Two latent variables carried out ca 95% of the analytical information and the results are in agreement with ICP-OES. (C) 2010 Elsevier B V. All rights reserved.