Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space.     

A Renormalization Group Classification of Nonstationary and/or Infinite Second Moment Diffusive Processes

Anomalous diffusion processes are often classified by their mean square displacement. If the mean square displacement grows linearly in time, the process is considered classical. If it grows like t ^β with β<1 or β>1, the process is considered subdiffusive or superdiffusive, respectively. Processes with infinite mean square displacement are considered superdiffusive. We begin by examining the ways in which power-law mean square displacements can arise; namely via non-zero drift, nonstationary increments, and correlated increments. Subsequently, we describe examples which illustrate that the above classification scheme does not work well when nonstationary increments are present. Finally, we introduce an alternative classification scheme based on renormalization groups. This scheme classifies processes with stationary increments such as Brownian motion and fractional Brownian motion in the same groups as the mean square displacement scheme, but does a better job of classifying processes with nonstationary increments and/or processes with infinite second moments such as α-stable Lévy motion. A numerical approach to analyzing data based on the renormalization group classification is also presented.     

The Thermodynamic Evolution of the Cosmological Event Horizon

By manipulating the integral expression for the proper radius R _e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR _e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR _e δR _e and δE _e in the horizon entropy S _e and enclosed energy E _e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T _e of the CEH at an arbitrary time in a flat FRW universe is E _e /S _e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T _e dS _e =PdV _e −dE _e , where V _e is the enclosed volume and P is the average cosmic pressure.     

Approximate <Emphasis Type="Italic">κ</Emphasis>-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C _s from the valence energy spectrum of particle and also for pseudospin symmetry constant C _ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.     

Synthesis and characterization of a polyaniline-modified SnO<Subscript>2</Subscript> nanocomposite

Polyaniline-modified tin oxide and tin oxide nanoparticles were synthesized using a solution route technique. The obtained pristine products were characterized with X-ray diffraction, thermogravimetric analysis, scanning electron microscopy, and optical absorption spectroscopy. Thermogravimetric analysis results showed that the polyaniline-modified SnO₂ nanoparticles exhibit higher thermal stability than the SnO₂ nanoparticles. Scanning electron microscopy analysis on the as-synthesized powders showed spherical particle in the range of 50–100 nm.     

Development of Aptamer Beacons for Rapid Presumptive Detection of <Emphasis Type="Italic">Bacillus</Emphasis> Spores

A library of 92 DNA aptamer sequences was developed against Bacillus anthracis (nonpathogenic Sterne strain) spores and anthrose sugar immobilized on magnetic beads. The selected DNA sequences were studied for similarities and potential binding pockets between the B. anthracis spore and anthrose aptamers. Several recurring loop structures were identified and tested for their potential to act as aptamer beacons when labeled with TYE 665 dye on their 5′ ends and Iowa Black quencher on their 3′ ends. Of these candidate sequences, two beacons designated BAS-6F and BAS-6R emerged which gave strong fluorescence responses at high spore concentrations (greater than 30,000 spores/ml). These aptamer beacons also detect B. cereus and B. thuringiensis spores with greater fluorescence intensity, but do not strongly detect vegetative cells from an array of other bacterial species. BAS-6F and 6R are also not capable of detecting pure anthrose, thereby probably ruling that epitope out as a spore surface target for these particular beacons. While not extremely sensitive, the BAS-6F and 6R aptamer beacons are potentially valuable for rapid presumptive detection of anthrax or Bacillus spores in suspect powders or bioterrorist activity where spore concentrations are anticipated to be high. The sequence similarities of these beacons to other published Bacillus spore aptamers are also discussed.     

Effect of hydrogen on surface texturing and crystallization of a-Si:H thin film irradiated by excimer laser

Hydrogenated amorphous silicon (a-Si:H) thin films have been considered for use in solar cell applications because of their significantly reduced cost compared to crystalline bulk silicon. However, their overall efficiency and stability are lower than that of their bulk crystalline counterpart. Limited work has been performed on simultaneously solving the efficiency and stability issues of a-Si:H. Previous work has shown that surface texturing and crystallization on a-Si:H thin film can be achieved through a single-step laser processing, which can potentially alleviate the disadvantages of a-Si:H in solar cell applications. In this study, hydrogenated and dehydrogenated amorphous silicon thin films deposited on glass substrates were irradiated by KrF excimer laser pulses and the effect of hydrogen on surface morphologies and microstructures is discussed. Sharp spikes are focused only on hydrogenated films, and the large-grained and fine-grained regions caused by two crystallization processes are also induced by presence of hydrogen. Enhanced light absorptance is observed due to light trapping based on surface geometry changes of a-Si:H films, while the formation of a mixture of nanocrystalline silicon and original amorphous silicon after crystallization suggests that the overall material stability can potentially improve. The relationship between crystallinity, fluence and number of pulses is also investigated. Furthermore, a step-by-step crystallization process is introduced to prevent the hydrogen from diffusing out in order to reduce the defect density, and the relationship between residue hydrogen concentration, fluence and step width is discussed. Finally, the combined effects show that the single-step process of surface texturing and step-by-step crystallization induced by excimer laser processing are promising for a-Si:H thin-film solar cell applications.     

Classical and quantum effects in spatially modulated optical parametric oscillators

We study the effects of transverse spatial modulations in a multimode degenerate optical parametric oscillator. Intracavity photonic crystals allow us to tune the instability threshold and improve entanglement above threshold. Here we compare such results with the case in which the modulation is in the injected field profile.     

Large-scale magnetic fields from inflation due to a <Emphasis Type="Italic">CPT</Emphasis>-even Chern–Simons-like term with Kalb–Ramond and scalar fields

We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the CPT-even dimension-six Chern–Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb–Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that magnetic fields on 1 Mpc scale with the field strength of ∼10⁻⁹ G at the present time can be induced.     

On Random Flights with Non-uniformly Distributed Directions

This paper deals with a new class of random flights in ℝ ^d , d≥2, characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature where the directions are taken according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter ν≥0, which gives the anisotropy of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function.