On the implication of Bell’s probability distribution and proposed experiments of quantum measurement

In derivating of Bell’s inequalities, the probability distribution is supposed to be a function only of a hidden variable. We point out that the true implication of the probability distribution of Bell’s correlation function is the distribution of joint measurement outcomes on the two sides. It is therefore a function of both the hidden variable and the settings. In this case, Bell’s inequalities fail. Our further analysis shows that Bell’s locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, and hence violation of Bell’s inequalities cannot rule out the existence of local hidden variable. To explain the results of EPR-type experiments, we suppose that a polarization-entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any nonlocal influence on it. Then several experiments are suggested to reveal the components of the polarization-entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with the same quantum state behave the same under the same measuring conditions.     

Theoretical prediction of absorbance spectra considering the particle size distribution using Mie theory and their comparison with the experimental UV–Vis spectra of synthesized nanoparticles

Under the frame work of Mie theory, a method has been developed to calculate the absorbance spectra of nanoparticles suspension containing a size distribution. The silver nanoparticles of two different sizes were first synthesized using a chemical reduction method and characterized by UV-Visible spectroscopy, dynamic light scattering, and transmission electron microscopy techniques. A model size-distribution were proposed and fitted to the experimental absorbance spectra using the described method. Better semiqualitative fitting to the experimental spectra were obtained by our proposed model in comparison to those obtained by single particle model.     

Constraints on distribution amplitudes of the η and η′ mesons in the light of new experimental results

Constraints on the distribution amplitudes of the SU _f (3) singlet η ₁ and octet η ₈ states are obtained from a comparison of the theoretical predictions for the η γ and η′γ electromagnetic transition form factors with experimental data of the CLEO and BaBar Collaborations. In calculations of the form factors F _η(η′)γ (Q ²) the power-suppressed corrections arising from the end-point integration regions x→0,1 are taken into account by employing the infrared renormalon approach. It is demonstrated that the power-suppressed corrections allow one to describe the data on the η γ and η′γ transitions within a framework of the SU _f (3) octet–singlet basis using one mixing angle for both the physical states and decay constants.     

Specific features of Raman spectra of III–V nanowhiskers

Raman spectra of GaAs nanowhiskers that are grown on different substrates and differ from one another by the content of the sphalerite and wurtzite phases have been investigated. Special attention has been focused on the manifestation of structural features in the scattering spectra of nanowhiskers. It has been established that the nanowhiskers are characterized both by random inclusions of wurtzite layers in the sphalerite structure and by the continuous growth in the wurtzite phase. The interpretation of the scattering spectrum agrees with the concept of summation of the dispersion curves of the sphalerite structure upon transition to the wurtzite structure, which leads to a transformation of zone-boundary modes at the L point of the Brillouin zone into zone-center modes of the wurtzite structure and, as a consequence, to the appearance of a number of new fundamental modes of different symmetries. An analysis of the Raman spectra has revealed the formation of the hexagonal 4H polytype in narrow layers of nanowhiskers due to a random packing of hexagonal layers. The coexistence of the sphalerite and wurtzite phases in GaAs nanowhiskers completely correlates with the photoluminescence spectra measured for the same samples.     

Solution of a torsional Schrödinger equation with a periodic potential of general form. The probability amplitude and probability density

Analytic expressions for the probability density of states of a molecule with internal rotation and the probability of finding the state in the potential well are derived for the first time. Two methods are proposed for assigning conformers to potential wells. A quantitative measure of localization and delocalization of a state in the potential well is introduced. The rotational symmetry number is generalized to the case of asymmetric rotation. On the basis of the localization criterion, a model is developed for calculating the internal rotation contribution to thermodynamic properties of individual conformers with low rotational barriers and/or at a high temperature.     

Excited states and absorption spectra of β-diketonate complexes of boron difluoride with aromatic substituents

In the approximation of the time-dependent electron density functional theory, we have studied using the quantum-chemical method the nature of excited states of boron difluoride acetylacetonate F₂BAA and its substituted derivatives that contain aromatic groups with one or two benzene cycles in the β-position. Optimization of the geometry of complexes show coplanar positions of cycles for all compounds, except for that with the substituent C₆H₃(CH₃)₂. Based on the calculated transition energies and oscillator strengths, we have simulated the absorption spectra in the prevacuum range. The calculated absorption spectra have been compared with the experimental spectra in the gas phase or in solutions. We show that, in the absorption spectra of complexes that contain substituents with one benzene cycle, the first three bands are caused by the transition of π electrons of the substituent to the LUMO of the chelate cycle. In complexes with two cycles in the substituent, the number of these transitions increases to five. As the π system becomes more extended, a bathochromic shift of the first absorption band and an increase in the transition probability are observed.     

Effect of relaxation rate on population distribution, EIT and refraction in Λ and V systems

In the three-level Λ-type and V-type systems, we find that the same pump-effect parameter R\left(=\dfrac{2|V_{c}|^{2}γ}{(ω_{ac}-ω_{c})^{2}+γ^{2}}\right) determines the population distributions, while the probe field leads to population fluctuations near the absorption peaks. With the increasing of the relaxation rate γ, the population distributions are shifted and their fluctuation amplitudes decrease. At the same time the electromagnetically induced transparency window becomes a broadened absorption peak, and the dispersion at the zero probe detuning changes from positive to negative. Large population fluctuation and non-fluctuation observed in different systems are attributed to the different relaxation rates.     

An overview of η and η' decays at BESIII

The world's largest sample of J/ψ events, 1.31 billion events accumulated at the BESIII detector, provides a unique opportunity to investigate η and η physics via two-body J/ψ radiative or hadronic decays. For many η decay channels the low background data samples are up to three orders of magnitude larger than collected in any previous experiment. Here we review the most significant results on η and η obtained at BESIII so far. The analyses range from detailed studies of common decay dynamics, observations of new radiative and Dalitz decays, and searches for rare/forbidden decays with sensitivity up to B～10-5. Finally, prospects of forthcoming runs at the J/ψ peak forη and η physics are discussed.     

Kα X-ray satellite spectra of Ti, V, Cr and Mn induced by photons

K X-ray emission spectra of Ti, V, Cr and Mn generated by photon excitation have been studied with a crystal spectrometer. The measured energy shifts of K_α satellite relative to the diagram line are compared with values obtained by electron excitation and with different theoretical estimates. The present experimental values of K_αL¹/K_αL⁰ relative intensities are compared with values obtained by electron excitation.      

Spectral broadening and electron–photon coupling in III–V infrared detectors of low dimensional quantum confined system

Present work explores the mid-IR photodetection mechanism in III–V quantum confined system in twofold ways. Firstly, it models the extent of spectral linewidth broadening of photo-detector. Secondly, it investigates whether a strong perturbation of light can modulate the electronic bandstructure. Photo-absorption mechanism in the detector correlated to reduced carrier lifetime in ground state leading to homogeneous spectral widening is calculated. Besides, contribution of non-uniform size and composition of quantum dots towards spectral broadening is modeled in order to get the envelop of inhomogeneously broadened photocurrent spectrum. Our model generates photocurrent spectrum with 1.4 μm broadening centered at 3.5 μm at 77 K for a DWELL-IP, which agrees with the experimental result. The calculated photocurrent spectral width of 1.3 μm for GaAs/AlGaAs Quantum Well (QW) centered at 8.31 μm at 77 K also supports experimental data. In addition, our calculation reveals the emergence of a broad resonant peak in the spectrum of QW-IP in far infrared region (20–50 μm) as the photon volume density increases up to 0.1% of carrier density inside the active region. We introduce a hybrid density-of-states for strongly coupled electron–photon system to explain both mid and far IR peak.     

Study ofA+A→0 with probability of reaction and diffusion in one dimension and in fractal substrata

We present Monte Carlo simulations of annihilation reactionA+A0 in one dimensional lattice and in three different fractal substrata. In the model, the particles diffuse independently and when two of them attempt to occupy the same substratum site, they react with a probabilityp. For different kinds of initial distributions and in the short an intermediate time regimes, the results for 0<p1 show that the density ofA particles approximately behaves as (t)=(t=0)f(t/t ₀), with the scaling functionf(x)1 forx1,f(x)x ^–y forx1. The crossover timet ₀, behaves ast _{0 0eff} ^–1y where theeffective initial density _0eff depends on (t=0) and on the kind of initial distribution. For a given substratum of spreading dimensiond _s, the exponenty(d _s/2<y<1) depends only onp and its value increases asp decreases (y1 whenp0). In the very long time regime it is expected thatp(t)t ^–ds/2 independently ofp.     

Experimental and theoretical study of linearly polarized Lorentz–Gauss beams with heterogeneous distribution

The unevenly distributed Lorentz–Gaussian beams are difficult to reproduce in practice, because they require modulation in both amplitude and phase terms. Here, a new linearly polarized Lorentz–Gauss beam modulated by a helical axicon(LGB-HA)is calculated, and the two various experimental generation methods of this beam, Fourier transform method(FTM) and complex-amplitude modulation(CAM) method, are depicted. Compared with the FTM, the CAM method can modulate the phase and amplitude simultaneously by only one reflection-type phase-only liquid crystal spatial light modulator.Both of the methods are coincident with the numerical results. Yet CAM is simpler, efficient, and has a higher degree of conformance through data comparison. In addition, considering some barriers exist in shaping and reappearing the complicated Lorentz–Gauss beam with heterogeneous distribution, the evolution regularities of the beams with different parameters(axial parameter, topological charge, and phase factor) were also implemented.     

Reconstruction of all-electron orbitals from one-electron pseudowave functions and calculations of the intensities of Si X-ray emission spectra of Si, β-SiC,stishovite, and β-cristobalite crystals

The intensities of Si X-ray emission spectra of Si, β-SiC, stishovite, and β-cristobalite crystals are calculated. The wave functions of the initial and final states are obtained in the framework of the density-functional theory with the use of the norm-conserving and ultrasoft pseudopotentials. The all-electron crystal orbitals are reconstructed from the one-electron pseudowave functions. The probabilities of X-ray emission transitions are calculated by reconstructing the all-electron orbitals in two different gauges, namely, the length and velocity gauges. The calculated intensities are compared with the experimental spectra and the partial densities of states.     

Estimating the entropy of liquids from atom–atom radial distribution functions: silica,beryllium fluoride and water

Molecular dynamics simulations of water, liquid beryllium fluoride and silica melt are used to study the accuracy with which the entropy of ionic and molecular liquids can be estimated from atom–atom radial distribution function data. The pair correlation entropy is demonstrated to be sufficiently accurate that the density–temperature regime of anomalous behaviour as well as the strength of the entropy anomaly can be predicted reliably for both ionic melts as well as different rigid-body pair potentials for water. Errors in the total thermodynamic entropy for ionic melts due to the pair correlation approximation are of the order of 10% or less for most state points, but can be significantly larger in the anomalous regime at very low temperatures. In the case of water, the rigid-body constraints result in larger errors in the pair correlation approximation, between 20 and 30%, for most state points. Comparison of the excess entropy, S _e, of ionic melts with the pair correlation entropy, S ₂, shows that the temperature dependence of S _e is well described by T ^?2/5 scaling across both the normal and anomalous regimes, unlike in the case of S ₂. The residual multiparticle entropy, ΔS = S _e ? S ₂, shows a strong negative correlation with tetrahedral order in the anomalous regime.     

The parton distribution functions of the photon and the structure functionF 2 γ (x,Q 2)

We present new parametrisations of the parton distribution functions of the photon including the first parametrisation in next-to-leading order QCD. We take into account some recent theoretical considerations pertaining to the gluon content of the photon,g ^γ. We argue that if an evolution is started at very lowQ ² and a fit to allF ₂ ^γ data performed with no constraints on the gluon distribution, then physically unreasonable gluon distributions may result. Our results support recent indications thatQ ₀ ² ≤1 GeV² is too low a value from which to start a perturbative evolution. Starting our evolution atQ ₀ ² =5.3 GeV², we evolve up inQ ² using a modified version of Rossi's Ansatz. The limited lever arm inQ ² leads to limited sensitivity to the QCD scale parameter Λ, though there is a preference for low values in the 0.1–0.2 GeV range. We also present new parametrisations of the singular asymptotic quark and gluon distribution functions of the photon which we believe are more accurate than those in current use.     

Effect of particle size and alloying with different metals on 57Fe Mössbauer spectra

Iron nanoparticles of various sizes have been synthesized using the chemical route which involves the preparation of iron bipyridine complexes in presence of different capping agents followed by thermal decomposition at 450°C in inert atmosphere. The bimetallic nanoalloys of Fe with Mg and Pd have also been prepared by following the same route. The resulting nanoparticles have been characterized by EDX-RF, XRD, AFM and ⁵⁷Fe Mössbauer spectroscopy. The appearance of quadrupole doublets in the Mössbauer spectra of Fe nanoparticles indicates the absence of magnetic interaction and variation in parameters is due to the varying particle size. The Mössbauer spectrum of Fe–Mg₂ bimetallic nanoalloy shows two doublets indicating the presence of superparamagnetism. The two doublets can be attributed to change in s-electron density of iron resulting from its two neighboring magnesium atoms. Fe–Pd nanoalloy Mössbauer spectrum is characterized by having a superparamagnetic doublet and a ferromagnetic sextet.     

Transmission of ∼10 keV electron beams through thin ceramic foils: Measurements and Monte Carlo simulations of electron energy distribution functions

Electron beams with particle energy of ~10 keV were sent through 300 nm thick ceramic (Si₃N₄ + SiO₂) foils and the resulting electron energy distribution functions were recorded using a retarding grid technique. The results are compared with Monte Carlo simulations performed with two publicly available packages, Geant4 and Casino v2.42. It is demonstrated that Geant4, unlike Casino, provides electron energy distribution functions very similar to the experimental distributions. Both simulation packages provide a quite precise average energy of transmitted electrons: we demonstrate that the maximum uncertainty of the calculated values of the average energy is 6% for Geant4 and 8% for Casino, taking into account all systematic uncertainties and the discrepancies in the experimental and simulated data.