Electron energy level statistics in graphene quantum dots

Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots [7] we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the experiment which confirms qualitatively interpretation of observed level statistics in terms of “Dirac billiards” without taking into account many-body effects. It is shown that edge effects are in general sufficient to produce the observed level distribution and that even strong bulk disorder does not change the results drastically. The article is published in the original.     

A transition in the spectral statistics of quantum optical model by different electromagnetic fields

In this paper, we have considered the effects of different quantized electromagnetic fields on the spectral statistics of two-level atoms. The Berry-Robnik distribution and the maximum likelihood estimation technique are used to analyze the effect of the mean photon numbers, the two level atoms numbers and also the quantum number of considered states on the fluctuation properties of different systems which are described by different sets of the Dicke Hamiltonian’s parameters. Our results describe the obvious effect of mean photon number on the spectral statistics and show more regular dynamics when this quantity reaches 700. Also, we observed universality in the spectral statistics of considered systems when the number of two level atoms approaches an unrealistic limit (N _A ~ 200) and there are some suggestions about the effect of the quantum number of selected levels and the atom-field coupling constant on level statistics.     

Donor ordering and the statistics of quantum dot level spacings and widths from full 3D self-consistent electronic structure

Using full 3D self-consistent electronic structure calculations of small (electron numberN 100) lateral quantum dots formed on GaAs–AlGaAs HEMT devices we calculate the statistics of level spacings Δε_pand tunneling coefficients Γ_pbetween leads and confined states of the dot. We employ random and ordered donor layer charge distributions, the latter generated through Monte Carlo variable range hopping simulations, as well as a homogeneous (jellium) ionic charge distribution, and examine the effects on these statistics.It has recently been argued that the statistics of the level spacings and widths follow from random matrix theory when the Hamiltonian is described by the Gaussian orthogonal ensemble (GOE) for zero magnetic fieldB, and by the Gaussian unitary ensemble (GUE) forBsufficiently large to break time reversal symmetry. Specifically it is argued that when the dot wave functions are expanded in an arbitrary basis the expansion coefficients, according to the postulate of Porter and Thomas, are uniformly distributed in Hilbert space.In our calculation we obtain statistics of level spacings and widths by generating many configurations of disordered and ordered donor charge. This corresponds to the experimental situation of thermal cycling of the device. We find that a pronounced transition occurs in the level spacing statistics between the completely disordered donor layer ensemble, which seems to be well described by random matrix theory, and the ordered ensemble which is dominated by secular variations in the coefficients. In particular, a shell structure in the levels, which results from approximate parabolicity in the self-consistent confining potential, is observed. This, and the effects of symmetry under inversion and azimuthal symmetry, are speculated to undermine level repulsion and result in Poisson statistics for the levels here at the band edge.Finally we find that distortions in the dot shape are markedly less significant in varying the widths (and level spacings) than calculations based on a hard wall potential for the dot predict. This suggests that the notion of invariant atomic structure for sufficiently small dots is not invalidated by the randomness inherent in donor positions and shape distortion but, on the contrary, a systematic study of dot structure is possible.     

Test of h1(1830) made of $$K^* \bar K^*$$ with the $$\eta _c \to \varphi K^* \bar K^*$$ decay

The transverse momentum distributions of final-state particles produced in collisions at energies available at the Large Hadron Collider (LHC) are studied by using the two-Boltzmann distribution and Tsallis statistics. Experimental distributions described by the two-Boltzmann distribution can be described by the Tsallis statistics. The two-temperature emission described by the two-Boltzmann distribution reflects temperature fluctuation of interacting system. The Tsallis statistics can describe the temperature fluctuation and the degree of non-equilibrium. The results calculated by the two-Boltzmann distribution and the Tsallis statistics are in agreement with the experimental data available at the LHC energies. In some cases, the two-Boltzmann distribution degenerates to (single) Boltzmann distribution.

     

Two-Dimensional Triplet Magnetoexcitons and a Magnetofermionic Condensate in the GaAs/AlGaAs Heterostructures

A fundamentally new collective state, namely, the magnetofermionic condensate, is discovered during photoexcitation of a sufficiently dense gas of long-lived triplet cyclotron magnetoexcitons in a twodimensional Hall insulator with a high electron mobility, a filling factor of ν = 2, and temperatures of T < 1 K. The condensed phase coherently interacts with an external electromagnetic field, exhibits superradiant properties in the recombination of correlated condensate electrons with heavy holes in the valence band, and spreads nondissipatively in the layer of a two-dimensional electron gas to macroscopical large distances, transferring an integer spin. The observed effects are explained in terms of a coherent condensate in a nonequilibrium system of two-dimensional fermions with a fully quantized energy spectrum, in which a degenerate ensemble of long-lived triplet magnetoexcitons obeying the Bose statistics is present.

     

Scattering by gamma-distributed phase screens

Abstract

The multipoint statistics of a joint gamma process are investigated. Analytical expressions are derived for the generating functions of the fourfold probability densities of the process and results are also obtained for its slope statistics. The results are used to characterize the wavefront distortion introduced into an incident beam of radiation by a phase changing screen and the scintillation index of the scattered intensity in the Fresnel region is calculated for various spectral models. Properties of the ray density functional are also investigated for the sub-fractal case when the wavefront is once differentiable.     

Modifications Induced by UV-Vis Irradiation on DNA Extract of Kiwifruit Investigated by Spectroscopic and Statistic Methods

ABSTRACT

Revealing molecular alterations induced on kiwifruit under UV-Vis irradiation requires a discussion of biochemical-cell infrared (IR) fingerprint (900 cm^?1–1800 cm^?1) bands characteristic of nucleic acids. FTIR-ATR spectroscopy and statistics and nondestructive methods for screening exposure effects induced by irradiation were used. There the irradiation influence on the main molecular bonds (i.e., ν(C-C), ν_s(PO₂?) and ν_as(PO₂?)) can be observed. Regression methods were used for statistical investigations. Two categories of variables were used: the absorbance measured at fixed wavenumber variables and the exposure dose. The bivariate correlations, partial correlations, and polynomial regression methods from SPSS were used for statistical investigations. The obtained results show that FTIR-ATR, in correlation with statistics techniques, might be useful to assess immediate radiation and oxidative-induced damage to nucleic acids. In this case IR spectroscopy can be used successfully to study conformational changes during DNA reversible denaturation especially on the sugar-phosphate vibrations domain.     

Photon-Added SU(1, 1) Coherent States and their Non-Classical Properties

The photon-added coherent states of Barut-Girardello and Perelomov types are constructed using Holstein-Primakoff realization of the su(1, 1) Lie algebra. Basic properties of the constructed states have been discussed. In addition, their non-classical features have been analyzed by computing photon detection probability distribution, Mandel Q-parameter and quadrature squeezing. It is shown that SU(1, 1) photon-added coherent states may exhibit sub-Poissonian statistics and quadrature squeezing for a chosen set of parameters. Moreover, it has been observed that their non-classical behavior increases as the number of added-photons increases.

     

Dark periods in the resonance fluorescence of a single Λ system

We use the quantum jump method to study the photon statistics of a single laser-driven atom in the configuration where both lower levels are strongly coupled to the common upper level. Under certain conditions we show that, for almost degenerate lower levels, light and dark periods occur which are similar to those of the well-known Dehmelt V system. Analytic results for their mean lengths and other statistical properties are given. For large separation of the lower levels we prove an interesting bunching property by the photons in the resonance fluorescence near the dark resonance. We propose a realistic system for which these effects may be observed.     

Photoconductivity derived from an exact modelling of the uncompensated one-donor model. I—simplified models revisited; and description of the method of solving the exact model equations

Abstract

Photoconductivity associated with a simple photoconductor model, containing one localised (donor) level, is taken up carefully through different approaches. Two simplified approaches are analysed, that are based on the assumption that some transitions between this level and the allowed bands can be neglected. The respective roles played by these hypotheses are specified through a hierarchical classification, and the limits of validity of the combined approximations are carefully stated. In a parallel direction, the related complete model is presented, which excludes no transitions and is based on Fermi—Dirac statistics. The resolution procedure of the resulting non-linear system of equations is then described, with the purpose of comparing the respective behaviours of all those models.     

Statistics of amplified light in periodically correlated layered systems with randomness

Abstract

We study the statistics of reflection and transmission coefficients of light in randomly layered amplifying media that are periodic on average. We are interested in one-dimensional universal scaling behaviours in such systems. Our study shows that while a homogeneous medium boundary condition is capable of reproducing universal scaling at low frequencies, a periodic medium boundary condition is necessary for high frequencies. Although the statistics depends on the boundary condition, the saturation length, where the reflection coefficient reaches a stationary distribution, and the localization length do not. Implications of these results are discussed.     

An Investigation of Signal Kinematical Region to Study Standard Model Higgs Boson Properties in the H → WW* → ℓvℓv Decay Channel in the ATLAS Experiment at the Large Hadron Collider at 13 TeV

A signal kinematical region is analyzed by the Higgs Boson Working Group (HWW) within the framework of a study of the Standard Model Higgs boson properties in the H → WW* → evεv decay channel in the ATLAS experiment on the Large Hadron Collider (LHC). The analysis is based on the full statistics of proton-proton collision data during exposures in 2015–2016 at the center-of-mass energy of 13 TeV. As compared to our previous analysis, the reconstruction software is updated and the simulation accuracy of backgrounds is improved. Events taken at low and high LHC luminosity are studied separately. In addition, the kinematics at the later stages of event selection is investigated in detail and systematic uncertainties are fully estimated. It is shown that the Monte Carlo modeling satisfactorily describes the experimental data at different selection stages. Kinematic distributions for hadron jets are studied also in the Z-boson control region, where the acquired data reach the order of ten million events. As compared to the previous investigation, the modeling accuracy of Z and background processes is noticeably improved, and events at low and high LHC luminosities are studied separately. Furthermore, all systematic uncertainties related to jets are estimated as well. As a whole, good agreement between experimental results and Monte Carlo simulation data is observed. No problems that would be caused by high luminosity are observed.

     

Statistical properties of wave transport through surface-disordered waveguides

We review some general statistical properties of wave transport through surface disordered waveguides. These systems are shown to present both striking similarities and differences with respect to quasi-one-dimensional waveguides with volume disorder. The statistical properties are analysed using extensive numerical calculations and random matrix theory results. The transport properties are characterized by the statistical behaviour of different transport coefficients that can be defined for both classical (light, microwaves, sound, etc.) and quantum (electrons) waves. In analogy with bulk-disordered systems, the behaviour of the waveguide conductance/resistance (defined for both classical and quantum waves) as a function of the system length defines three different transport regimes: ballistic, diffusive and localization. However, the coupling between waveguide modes presents significant differences with respect to the coupling induced by volume defects. For any incoming mode, there is a strong preference for the forward propagation through the lowest mode. For narrow waveguides, the statistics of reflection coefficients (reflected speckle pattern) present strong finite-size effects which can be surprisingly well described by random matrix theory. Special attention is paid to the fundamental problem of the transition between different regimes. The long-standing problems of the phase randomization process between ballistic and diffusive regimes and the evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) are also discussed.     

Graphical thresholding procedure and optimal light level estimation for spatially resolved photon counting with EMCCDs

Thanks to the electron multiplying function that can effectively convert the weak incident photon signal to amplified electron output, electron multiplying charged-coupled devices (EMCCDs) are becoming useful and popular detectors in photon counting regimes necessitating also spatial resolution. A multi-imaging strategy has been already proposed and experimentally tested to improve the accuracy of photon counting with an EMCCD, by taking into account the random nature of its on-chip gain and the possibility of multiple photodetection events on 1 pixel. In this paper, referring to the thresholding procedure developed for photon counting, we present a clear graphical method for the threshold and the optimal light level estimations. Thanks to the graphical visualization of the probabilities involved in the detection errors on 1 pixel, we are able to derive in a straightforward way and for any EMCCD, the threshold level and thus the best mean level of illumination to be used in order to minimize the false detection probabilities that might ruin the image statistics, especially in cases where quantum spatial effects might be observed.     

Zusammenhänge Zwischen Radonanomalien und Schwarm-Erdbeben im Oberen Vogtland

Abstract

The results of continuous radon measurements in soil air and the water of a mineral spring at Bad Brambach are presented. They are discussed in connection with meteorological, hydrological parameters, and seismic events with magnitudes <3. The atmospheric pressure (especially pressure gradient), the temperature, and the groundwater level gradient have a significant influence onto radon activity of soil air.

The gamma-activity in spring water is influenced by the water flow rate only.

The results show that the soil air (mean Rn activity 130 Bq · l^?1) and especially the water of the Radonquelle of Bad Brambach (mean Rn activity 25 kBq · l^?1) react upon micro earthquakes with small epicentral distances. Frequently there are precursor effects, that means radon maxima due to the building up of tectonic stress/strain.

About 60% of the seismic events had been attended by radon anomalies during the registration period.

The long term measurements will be continued to investigate possible influences of earthquakes with higher epicentral distances and magnitudes >5 onto the radon regime of the bad Brambach area.     

Single-molecule spectroscopy of radical pairs,a theoretical treatment and experimental considerations

ABSTRACT

In this work, we propose to extend the scope of single-molecule spectroscopy to spin chemistry investigations of single radical pairs. A consistent theory of single-molecule spectroscopy on single radical pairs is proposed, which allows one to show that bunching phenomena are affected by singlet–triplet interconversion in radical pairs, which is, in turn, affected by local and external magnetic fields. A detailed study on the feasibility of such experiments with single flavin adenine dinucleotide, FAD, molecules is presented. We conclude that the observation of magnetic field effects on single FAD molecules is feasible but experimentally challenging for measurements on integrated fluorescence intensity and fluorescence event statistics.     

The Impact of Ozone on the 15N Incorporation and Nitrogen Assimilation of Wheat and Maize

Abstract

Young wheat (C3) and maize (C4) plants were exposed to near-ambient concentrations of ozone in open-top chambers in order to investigate the possible effects of ozone on nitrogen metabolism. Nitrogen was supplied to the plants by adding ¹⁵N-labelled tracer substances via the soil substrate. Enzyme activities (NADH nitrate reductase, nitrite reductase, glutamine synthetase and NADH glutamate dehydrogenase) and the incorporation of ¹⁵N were determined.

The findings show that nitrogen metabolism was affected by O₃, however, there were distinct differences between the two species. In plants treated with O₃, NADH nitrate reductase activity in maize leaves was reduced, while NR activity in wheat leaves only slightly declined. Only minor changes were observed with respect to the activities of nitrite reductase, glutamine synthetase and NADH glutamate dehydrogenase.

Feeding experiments using ¹⁵NO₃ ^? showed that the incorporation of nitrate nitrogen in wheat plants exposed to ozone remains virtually unchanged, whereas in maize plants reduced incorporation rates were observed for nitrate nitrogen. The incorporation of ammonium nitrogen was distinctly increased in wheat and maize by the impact of ozone.

When investigating pigment contents, reduced levels of chlorophyll a and b and carotenoids were observed, whereas the pigment content of wheat leaves remained unchanged. These results indicate that young maize plants are more susceptible than wheat plants to short-term ozone exposure.     

Level-crossing statistics and production in low Reynolds number wall turbulence

Statistical properties at velocity level crossings are analysed in a low Reynolds number fully developed turbulent channel flow. Emphasis is placed on local production statistics conditioned by fixed amplitudes of the streamwise u and wall-normal v velocity components. Direct numerical simulations performed in large computational domains are used for this purpose. The Reynolds number based on the channel half width and the shear velocity varies from 180 to 1100. Particular attention is paid to correctly determine the conditional quantities at level crossings of u and v velocity fluctuations, to prevent biasing effects. Level crossings along the longitudinal x and spanwise z directions in homogeneous planes are introduced together with different characterisations, such as directional and contour crossings. The frequency of events detected at fixed thresholds follows a Gaussian model acceptably well. There is more level-crossing activity in the spanwise direction than in the streamwise. The mean conditional production distributions are dissymmetrical with respect to the level-crossing thresholds in the low buffer and viscous sublayers. These statistics differ significantly from a statistical model that assumes joint normality between u and v. There is a clear but relatively mild Reynolds number dependence of the conditional expected means of u and v that do not scale with inner, outer or mixed variables. The Reynolds number sensitivity of these statistics increases towards the edge of the wall layer.     

An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)