Search results for: Dirac fermion systems

Authors: Vipin Kumar, Girish S. Setlur

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Graphene has been recognized as a promising 2D material with many new properties. However, pristine graphene is gapless which hinders its direct application towards graphene-based semiconducting devices. Graphene is a zero-gapp and linearly dispersing semiconductor. Massless charge carriers (quasi-particles) in graphene obey the relativistic Dirac equation. These Dirac fermions show very unusual physical properties such as electronic, optical and transport. Graphene is analogous to two-level atomic systems and conventional semiconductors. We may expect that graphene-based systems will also exhibit phenomena that are well-known in two-level atomic systems and in conventional semiconductors. Rabi oscillation is a nonlinear optical phenomenon well-known in the context of two-level atomic systems and also in conventional semiconductors. It is the periodic exchange of energy between the system of interest and the electromagnetic field. The present work describes the phenomenon of Rabi oscillations in graphene based systems. Rabi oscillations have already been described theoretically and experimentally in the extensive literature available on this topic. To describe Rabi oscillations they use an approximation known as rotating wave approximation (RWA) well-known in studies of two-level systems. RWA is valid only near conventional resonance (small detuning)- when the frequency of the external field is nearly equal to the particle-hole excitation frequency. The Rabi frequency goes through a minimum close to conventional resonance as a function of detuning. Far from conventional resonance, the RWA becomes rather less useful and we need some other technique to describe the phenomenon of Rabi oscillation. In conventional systems, there is no second minimum - the only minimum is at conventional resonance. But in graphene we find anomalous Rabi oscillations far from conventional resonance where the Rabi frequency goes through a minimum that is much smaller than the conventional Rabi frequency. This is known as anomalous Rabi frequency and is unique to graphene systems. We have shown that this is attributable to the pseudo-spin degree of freedom in graphene systems. A new technique, which is an alternative to RWA called asymptotic RWA (ARWA), has been invoked by our group to discuss the phenomenon of Rabi oscillation. Experimentally accessible current density shows different types of threshold behaviour in frequency domain close to the anomalous Rabi frequency depending on the system chosen. For single layer graphene, the exponent at threshold is equal to 1/2 while in case of bilayer graphene, it is computed to be equal to 1. Bilayer graphene shows harmonic (anomalous) resonances absent in single layer graphene. The effect of asymmetry and trigonal warping (a weak direct inter-layer hopping in bilayer graphene) on these oscillations is also studied in graphene systems. Asymmetry has a remarkable effect only on anomalous Rabi oscillations whereas the Rabi frequency near conventional resonance is not significantly affected by the asymmetry parameter. In presence of asymmetry, these graphene systems show Rabi-like oscillations (offset oscillations) even for vanishingly small applied field strengths (less than the gap parameter). The frequency of offset oscillations may be identified with the asymmetry parameter.

Keywords: graphene, Bilayer graphene, Rabi oscillations, Dirac fermion systems

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Authors: Debjit Dutta, P. Roy, O. Panella

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In recent years, non Hermitian interaction in non relativistic as well as relativistic quantum mechanics have been examined from various aspect. We can observe interesting fact that for such systems a class of potentials, namely the PT symmetric and η-pseudo Hermitian admit real eigenvalues despite being non Hermitian and analogues of those system have been experimentally verified. Point to be noted that relativistic non Hermitian (PT symmetric) interactions can be realized in optical structures and also there exists photonic realization of the (1 + 1) dimensional Dirac oscillator. We have thoroughly studied generalized Dirac oscillators with non Hermitian interactions in (1 + 1) dimensions. To be more specific, we have examined η pseudo Hermitian interactions within the framework of generalized Dirac oscillator in (1 + 1) dimensions. In particular, we have obtained a class of interactions which are η-pseudo Hermitian and the metric operator η could have been also found explicitly. It is possible to have exact solutions of the generalized Dirac oscillator for some choices of the interactions. Subsequently we have employed the mapping between the generalized Dirac oscillator and the Jaynes Cummings (JC) model by spin flip to obtain a class of exactly solvable non Hermitian JC as well as anti Jaynes Cummings (AJC) type models.

Keywords: Dirac oscillator, non-Hermitian quantum system, Hermitian, relativistic

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Beatriz Muñiz Cano, J. Ripoll Sau, D. Pacile, P. M. Sheverdyaeva, P. Moras, J. Camarero, R. Miranda, M. Garnica, M. A. Valbuena

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Graphene, in its pristine state, is a semiconductor with a zero band gap and massless Dirac fermions carriers, which conducts electrons like a metal. Nevertheless, the absence of a bandgap makes it impossible to control the material’s electrons, something that is essential to perform on-off switching operations in transistors. Therefore, it is necessary to generate a finite gap in the energy dispersion at the Dirac point. Intense research has been developed to engineer band gaps while preserving the exceptional properties of graphene, and different strategies have been proposed, among them, quantum confinement of 1D nanoribbons or the introduction of super periodic potential in graphene. Besides, in the context of developing new 2D materials and Van der Waals heterostructures, with new exciting emerging properties, as 2D transition metal chalcogenides monolayers, it is fundamental to know any possible interaction between chalcogenide atoms and graphene-supporting substrates. In this work, we report on a combined Scanning Tunneling Microscopy (STM), Low Energy Electron Diffraction (LEED), and Angle-Resolved Photoemission Spectroscopy (ARPES) study on a new superstructure when Te is evaporated (and intercalated) onto graphene over Ir(111). This new superstructure leads to the electronic doping of the Dirac cone while the linear dispersion of massless Dirac fermions is preserved. Very interestingly, our ARPES measurements evidence a large band gap (~400 meV) at the Dirac point of graphene Dirac cones below but close to the Fermi level. We have also observed signatures of the Dirac point binding energy being tuned (upwards or downwards) as a function of Te coverage.

Keywords: angle resolved photoemission spectroscopy, ARPES, graphene, spintronics, spin-orbitronics, 2D materials, transition metal dichalcogenides, TMDCs, TMDs, LEED, STM, quantum materials

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Authors: Mohammad Saeed Bahramy

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Transition metal dichalcogenides have experienced a resurgence of interest in the past few years owing to their rich properties, ranging from metals and superconductors to strongly spin-orbit-coupled semiconductors and charge-density-wave systems. In all these cases, the transition metal d-electrons mainly determine the ground state properties. This presentation focuses on the chalcogen-derived states. Combining density-functional theory calculations with spin- and angle-resolved photoemission, it is shown that these states generically host a coexistence of type I and type II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. It will be discussed how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across many compounds. Our finding opens a new route to design topological materials with advanced functionalities.

Keywords: topology, electronic structure, Dirac semimetals, transition metal dichalcogenides

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Authors: N. Messai, A. Boumali

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In this work, we aim to solve the two dimensional Kemmer equation including Dirac oscillator interaction term, in the background space-time generated by a cosmic string which is submitted to an uniform magnetic field. Eigenfunctions and eigenvalues of our problem have been found and the influence of the cosmic string space-time on the energy spectrum has been analyzed.

Keywords: Kemmer oscillator, cosmic string, Dirac oscillator, eigenfunctions

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Authors: Minna Theres James, Nirmal K Sebastian, Shoubhik Mandal, Pramita Mishra, R Ganesan, P S Anil Kumar

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We report the temperature-dependent evolution of Raman spectra of type-II Dirac semimetal (DSM) NiTe2 (001) in the form of bulk single crystal and a nanoflake (200 nm thick) for the first time. A physical model that can quantitatively explain the evolution of out of plane A1g and in-plane E1g Raman modes is used. The non-linear variation of peak positions of the Raman modes with temperature is explained by anharmonic three-phonon and four-phonon processes along with thermal expansion of the lattice. We also observe prominent effect of electron-phonon coupling from the variation of FWHM of the peaks with temperature, indicating the metallicity of the samples. Raman mode E1 1g corresponding to an in plane vibration disappears on decreasing the thickness from bulk to nanoflake.

Keywords: raman spectroscopy, type 2 dirac semimetal, nickel telluride, phonon-phonon coupling, electron phonon coupling, transition metal dichalcogonide

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Authors: Thandar Zaw Win, Cho Win Aung, Gaurav Khandal, Sabyasachi Ghosh

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Systematic and comparative research on Lorenz ratios for graphene and nonrelativistic systems has been studied to identify their Wiedemann-Franz law violation domain. Fermi energy and temperature are the main governing parameters for deciding the values of the Lorenz ratio, which is basically thermal conductivity divided by electrical conductivity times temperature times Lorenz number. Metals as three-dimensional nonrelativistic electron gas are located at higher Fermi-energy by temperature domain, where Lorenz ratio remains one. Hence, they obey the Wiedemann-Franz law. By creating higher doping in a two-dimensional graphene system, one can again reach a higher Fermi-energy by temperature domain and get a constant Lorenz ratio. For both graphene and nonrelativistic systems, the Lorenz ratio goes below one if we go lower Fermi-energy by temperature domain, which is possible for the graphene system by decreasing the doping concentration. Experimentally observed greater than one Lorenz ratio in this lower Fermi-energy by temperature domain or Dirac Fluid domain indicates that nonfluid expressions of Lorenz ratio should be replaced by fluidtype expressions. We have noticed a divergent trend of Lorenz ratio in the Dirac Fluid domain using its fluid-type expression, and it matches the trend of experimental data.

Keywords: graphene, Lorentz ratio, specific heat, Wiedeann-Franz law

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Authors: M. Asato, C. Liu, N. Fujima, T. Hoshino, Y. Chen, T. Mohri

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We study the temperature dependence of the interaction energies (IEs) of X (=Ru, Rh) impurities in Pd, due to the Fermi-Dirac (FD) distribution and the thermal vibration effect by the Debye-Grüneisen model. The n-body (n=2~4) IEs among X impurities in Pd, being used to calculate the internal energies in the free energies of the Pd-rich PdX alloys, are determined uniquely and successively from the lower-order to higher-order, by the full-potential Korringa-Kohn-Rostoker Green’s function method (FPKKR), combined with the generalized gradient approximation in the density functional theory. We found that the temperature dependence of IEs due to the FD distribution, being usually neglected, is very important to reproduce the X-concentration dependence of the observed solvus temperatures of the Pd-rich PdX (X=Ru, Rh) alloys.

Keywords: full-potential KKR-green’s function method, Fermi-Dirac distribution, GGA, phase diagram of Pd-rich PdX (X=Ru, Rh) alloys, thermal vibration effect

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Authors: Zhipeng Dong, Jing Guo

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Graphene-semiconductor contacts have been extensively studied recently, both as a stand-alone diode device for potential applications in photodetectors and solar cells, and as a building block to vertical transistors. Graphene is a two-dimensional nanomaterial with vanishing density-of-states at the Dirac point, which differs from conventional metal. In this work, image-charge-induced barrier lowering (BL) in graphene-semiconductor contacts is studied and compared to that in metal Schottky contacts. The results show that despite of being a semimetal with vanishing density-of-states at the Dirac point, the image-charge-induced BL is significant. The BL value can be over 50% of that of metal contacts even in an intrinsic graphene contacted to an organic semiconductor, and it increases as the graphene doping increases. The dependences of the BL on the electric field and semiconductor dielectric constant are examined, and an empirical expression for estimating the image-charge-induced BL in graphene-semiconductor contacts is provided.

Keywords: graphene, semiconductor materials, schottky barrier, image charge, contacts

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Authors: Andrey Davydov, Konstantin Sveshnikov, Yulia Voronina

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There is now a lot of interest to the non-perturbative QED-effects, caused by diving of discrete levels into the negative continuum in the supercritical static or adiabatically slowly varying Coulomb fields, that are created by the localized extended sources with Z > Z_cr. Such effects have attracted a considerable amount of theoretical and experimental activity, since in 3+1 QED for Z > Z_cr,1 ≈ 170 a non-perturbative reconstruction of the vacuum state is predicted, which should be accompanied by a number of nontrivial effects, including the vacuum positron emission. Similar in essence effects should be expected also in both 2+1 D (planar graphene-based hetero-structures) and 1+1 D (one-dimensional ‘hydrogen ion’). This report is devoted to the study of such essentially non-perturbative vacuum effects for the supercritical Dirac-Coulomb systems in 1+1D and 2+1D, with the main attention drawn to the vacuum polarization energy. Although the most of works considers the vacuum charge density as the main polarization observable, vacuum energy turns out to be not less informative and in many respects complementary to the vacuum density. Moreover, the main non-perturbative effects, which appear in vacuum polarization for supercritical fields due to the levels diving into the lower continuum, show up in the behavior of vacuum energy even more clear, demonstrating explicitly their possible role in the supercritical region. Both in 1+1D and 2+1D, we explore firstly the renormalized vacuum density in the supercritical region using the Wichmann-Kroll method. Thereafter, taking into account the results for the vacuum density, we formulate the renormalization procedure for the vacuum energy. To evaluate the latter explicitly, an original technique, based on a special combination of analytical methods, computer algebra tools and numerical calculations, is applied. It is shown that, for a wide range of the external source parameters (the charge Z and size R), in the supercritical region the renormalized vacuum energy could significantly deviate from the perturbative quadratic growth up to pronouncedly decreasing behavior with jumps by (-2 x mc^2), which occur each time, when the next discrete level dives into the negative continuum. In the considered range of variation of Z and R, the vacuum energy behaves like ~ -Z^2/R in 1+1D and ~ -Z^3/R in 2+1D, exceeding deeply negative values. Such behavior confirms the assumption of the neutral vacuum transmutation into the charged one, and thereby of the spontaneous positron emission, accompanying the emergence of the next vacuum shell due to the total charge conservation. To the end, we also note that the methods, developed for the vacuum energy evaluation in 2+1 D, with minimal complements could be carried over to the three-dimensional case, where the vacuum energy is expected to be ~ -Z^4/R and so could be competitive with the classical electrostatic energy of the Coulomb source.

Keywords: non-perturbative QED-effects, one- and two-dimensional Dirac-Coulomb systems, supercritical fields, vacuum polarization

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Authors: Md. Shah Alam

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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

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Authors: Ahmad Almajid

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The idea of unifying quantum mechanics with general relativity is still a dream for many researchers, as physics has only two paths, no more. Einstein's path, which is mainly based on particle mechanics, and the path of Paul Dirac and others, which is based on wave mechanics, the incompatibility of the two approaches is due to the radical difference in the initial assumptions and the mathematical nature of each approach. Logical thinking in modern physics leads us to two problems: - In quantum mechanics, despite its success, the problem of measurement and the problem of wave function interpretation is still obscure. - In special relativity, despite the success of the equivalence of rest-mass and energy, but at the speed of light, the fact that the energy becomes infinite is contrary to logic because the speed of light is not infinite, and the mass of the particle is not infinite too. These contradictions arise from the overlap of relativistic and quantum mechanics in the neighborhood of the speed of light, and in order to solve these problems, one must understand well how to move from relativistic mechanics to quantum mechanics, or rather, to unify them in a way different from Dirac's method, in order to go along with God or Nature, since, as Einstein said, "God doesn't play dice." From De Broglie's hypothesis about wave-particle duality, Léon Brillouin's definition of the new proper time was deduced, and thus the quantum Lorentz factor was obtained. Finally, using the Euler-Lagrange equation, we come up with new equations in quantum mechanics. In this paper, the two problems in modern physics mentioned above are solved; it can be said that this new approach to quantum mechanics will enable us to unify it with general relativity quite simply. If the experiments prove the validity of the results of this research, we will be able in the future to transport the matter at speed close to the speed of light. Finally, this research yielded three important results: 1- Lorentz quantum factor. 2- Planck energy is a limited case of Einstein energy. 3- Real quantum mechanics, in which new equations for quantum mechanics match and exceed Dirac's equations, these equations have been reached in a completely different way from Dirac's method. These equations show that quantum mechanics is a limited case of relativistic mechanics. At the Solvay Conference in 1927, the debate about quantum mechanics between Bohr, Einstein, and others reached its climax, while Bohr suggested that if particles are not observed, they are in a probabilistic state, then Einstein said his famous claim ("God does not play dice"). Thus, Einstein was right, especially when he didn't accept the principle of indeterminacy in quantum theory, although experiments support quantum mechanics. However, the results of our research indicate that God really does not play dice; when the electron disappears, it turns into amicable particles or an elastic medium, according to the above obvious equations. Likewise, Bohr was right also, when he indicated that there must be a science like quantum mechanics to monitor and study the motion of subatomic particles, but the picture in front of him was blurry and not clear, so he resorted to the probabilistic interpretation.

Keywords: lorentz quantum factor, new, planck’s energy as a limiting case of einstein’s energy, real quantum mechanics, new equations for quantum mechanics

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Authors: Anna V. Zaporozhchenko, Dmytro Kutnyakhov, Katherina Medjanik, Christian Tusche, Hans-Joachim Elmers, Olena Fedchenko, Sergey Chernov, Martin Ellguth, Sergej A. Nepijko, Gerd Schoenhense

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Graphene reveals a unique electronic structure that predetermines many intriguing properties such as massless charge carriers, optical transparency and high velocity of fermions at the Fermi level, opening a wide horizon of future applications. Hence, a detailed investigation of the electronic structure of graphene is crucial. The method of choice is angular resolved photoelectron spectroscopy ARPES. Here we present experiments using time-of-flight (ToF) momentum microscopy, being an alternative way of ARPES using full-field imaging of the whole Brillouin zone (BZ) and simultaneous acquisition of up to several 100 energy slices. Unlike conventional ARPES, k-microscopy is not limited in simultaneous k-space access. We have recorded the whole first BZ of graphene on Ir(111) including all six Dirac cones. As excitation source we used synchrotron radiation from BESSY II (Berlin) at the U125-2 NIM, providing linearly polarized (both polarizations p- and s-) VUV radiation. The instrument uses a delay-line detector for single-particle detection up the 5 Mcps range and parallel energy detection via ToF recording. In this way, we gather a 3D data stack I(E,kx,ky) of the full valence electronic structure in approx. 20 mins. Band dispersion stacks were measured in the energy range of 14 eV up to 23 eV with steps of 1 eV. The linearly-dispersing graphene bands for all six K and K’ points were simultaneously recorded. We find clear features of hybridization with the substrate, in particular in the linear dichroism in the angular distribution (LDAD). Recording of the whole Brillouin zone of graphene/Ir(111) revealed new features. First, the intensity differences (i.e. the LDAD) are very sensitive to the interaction of graphene bands with substrate bands. Second, the dark corridors are investigated in detail for both, p- and s- polarized radiation. They appear as local distortions of photoelectron current distribution and are induced by quantum mechanical interference of graphene sublattices. The dark corridors are located in different areas of the 6 Dirac cones and show chirality behaviour with a mirror plane along vertical axis. Moreover, two out of six show an oval shape while the rest are more circular. It clearly indicates orientation dependence with respect to E vector of incident light. Third, a pattern of faint but very sharp lines is visible at energies around 22eV that strongly remind on Kikuchi lines in diffraction. In conclusion, the simultaneous study of all six Dirac cones is crucial for a complete understanding of dichroism phenomena and the dark corridor.

Keywords: band structure, graphene, momentum microscopy, LDAD

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Authors: Vedanki Khandenwal, Pawan Srivastava, Kartick Tarafder, Subhasis Ghosh

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We present here the experimental realization of controlled doping of graphene monolayers through charge transfer by trapping selected organic molecules between the graphene layer and underlying substrates. This charge transfer between graphene and trapped molecule leads to controlled n-type or p-type doping in monolayer graphene (MLG), depending on whether the trapped molecule acts as an electron donor or an electron acceptor. Doping controllability has been validated by a shift in corresponding Raman peak positions and a shift in Dirac points. In the transfer characteristics of field effect transistors, a significant shift of Dirac point towards positive or negative gate voltage region provides the signature of p-type or n-type doping of graphene, respectively, as a result of the charge transfer between graphene and the organic molecules trapped within it. In order to facilitate the charge transfer interaction, it is crucial for the trapped molecules to be situated in close proximity to the graphene surface, as demonstrated by findings in Raman and infrared spectroscopies. However, the mechanism responsible for this charge transfer interaction has remained unclear at the microscopic level. Generally, it is accepted that the dipole moment of adsorbed molecules plays a crucial role in determining the charge-transfer interaction between molecules and graphene. However, our findings clearly illustrate that the doping effect primarily depends on the reactivity of the constituent atoms in the adsorbed molecules rather than just their dipole moment. This has been illustrated by trapping various molecules at the graphene−substrate interface. Dopant molecules such as acetone (containing highly reactive oxygen atoms) promote adsorption across the entire graphene surface. In contrast, molecules with less reactive atoms, such as acetonitrile, tend to adsorb at the edges due to the presence of reactive dangling bonds. In the case of low-dipole moment molecules like toluene, there is a lack of substantial adsorption anywhere on the graphene surface. Observation of (i) the emergence of the Raman D peak exclusively at the edges for trapped molecules without reactive atoms and throughout the entire basal plane for those with reactive atoms, and (ii) variations in the density of attached molecules (with and without reactive atoms) to graphene with their respective dipole moments provides compelling evidence to support our claim. Additionally, these observations were supported by first principle density functional calculations.

Keywords: graphene, doping, charge transfer, liquid phase exfoliation

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Authors: Anil Kumar, Rajnish Kaur, Mateusz Czyzycki, Alessandro Migilori, Andreas Germanos Karydas, Sanjiv Puri

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The radiative decay of Li(i=1-3) sub-shell vacancies produced through photoionization results in production of the characteristic emission spectrum comprising several X-ray lines, whereas non-radiative vacancy decay results in Auger electron spectrum. Accurate reliable data on the Li(i=1-3) sub-shell X-ray production (XRP) cross sections is of considerable importance for investigation of atomic inner-shell ionization processes as well as for quantitative elemental analysis of different types of samples employing the energy dispersive X-ray fluorescence (EDXRF) analysis technique. At incident photon energies in vicinity of the absorption edge energies of an element, the many body effects including the electron correlation, core relaxation, inter-channel coupling and post-collision interactions become significant in the photoionization of atomic inner-shells. Further, in case of compounds, the characteristic emission spectrum of the specific element is expected to get influenced by the chemical environment (coordination number, oxidation state, nature of ligand/functional groups attached to central atom, etc.). These chemical effects on L X-ray fluorescence parameters have been investigated by performing the measurements at incident photon energies much higher than the Li(i=1-3) sub-shell absorption edge energies using EDXRF spectrometers. In the present work, the cross sections for production of the Lk(k= γ2,3, γ4) X-rays have been measured for some compounds of 66Dy, namely, Dy2O3, Dy2(CO3)3, Dy2(SO4)3.8H2O, DyI2 and Dy metal by tuning the incident photon energies few eV above the L1 absorption-edge energy in order to investigate the influence of chemical effects on these cross sections in presence of the many body effects which become significant at photon energies close to the absorption-edge energies. The present measurements have been performed under vacuum at the IAEA end-station of the X-ray fluorescence beam line (10.1L) of ELETTRA synchrotron radiation facility (Trieste, Italy) using self-supporting pressed pellet targets (1.3 cm diameter, nominal thicknesses ~ 176 mg/cm2) of 66Dy compounds (procured from Sigma Aldrich) and a metallic foil of 66Dy (nominal thickness ~ 3.9 mg/cm2, procured from Good Fellow, UK). The present measured cross sections have been compared with theoretical values calculated using the Dirac-Hartree-Slater(DHS) model based fluorescence and Coster-Kronig yields, Dirac-Fock(DF) model based X-ray emission rates and two sets of L1 sub-shell photoionization cross sections based on the non-relativistic Hartree-Fock-Slater(HFS) model and those deduced from the self-consistent Dirac-Hartree-Fock(DHF) model based total photoionization cross sections. The present measured XRP cross sections for 66Dy as well as for its compounds for the L2,3 and L4 X-rays, are found to be higher by ~14-36% than the two calculated set values. It is worth to be mentioned that L2,3 and L4 X-ray lines are originated by filling up of the L1 sub-shell vacancies by the outer sub-shell (N2,3 and O2,3) electrons which are much more sensitive to the chemical environment around the central atom. The present observed differences between measured and theoretical values are expected due to combined influence of the many-body effects and the chemical effects.

Keywords: chemical effects, L X-ray production cross sections, Many body effects, Synchrotron radiation

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Authors: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: Ahmet Kaya

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Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: quantum physics, Hamiltonian system, path integral, tensor product, ruin probability

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Authors: Peter Jean-Paul, Shanaz Wahid

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The problem of division by zero can be stated as: “what is the value of 0 x 1/0?” This expression has been considered undefined by mathematicians because it can have two equally valid solutions either 0 or 1. Recently semi-structured complex number set was invented to solve “division by zero”. However, whilst the number set had some merits it was considered to have a poor theoretical foundation and did not provide a quality solution to “division by zero”. Moreover, the set lacked consistency in simple algebraic calculations producing contradictory results when dividing by zero. To overcome these issues this research starts by treating the expression " 0 x 1/0" as a quantum mechanical system that produces two tangled results 0 and 1. Dirac Notation (a tool from quantum mechanics) was then used to redefine the unstructured unit p in semi-structured complex numbers so that p represents the superposition of two results (0 and 1) and collapses into a single value when used in algebraic expressions. In the process, this paper describes a new number set called Quantum Semi-structured Complex Numbers that provides a valid solution to the problem of “division by zero”. This research shows that this new set (1) forms a “Field”, (2) can produce consistent results when solving division by zero problems, (3) can be used to accurately describe systems whose mathematical descriptions involve division by zero. This research served to provide a firm foundation for Quantum Semi-structured Complex Numbers and support their practical use.

Keywords: division by zero, semi-structured complex numbers, quantum mechanics, Hilbert space, Euclidean space

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Authors: Habtamu Anagaw Muluneh, Gebregziabher Kahsay, Tamiru Negussie

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Theoretical study of the density of state, condensation energy, specific heat, and magnetization in a spin-triplet superconductor are the main goals of this work. Utilizing the retarded double-time temperature-dependent Green's function formalism and building a model Hamiltonian for the system at hand, we were able to derive the expressions for the parameters mentioned above. The phase diagrams are plotted using MATLAB scripts. From the phase diagrams, the density of electrons increases as the excitation energy increases, and the maximum excitation energy is equal to the superconducting gap, but it decreases when the value exceeds the gap and finally becomes the same as the density of the normal state. On the other hand, the condensation energy decreases with the increase in temperature and attains its minimum value at the superconducting transition temperature but increases with the increase in superconducting transition temperature (TC) and finally becomes zero, implying the superconducting energy is equal to the normal state energy. The specific heat increases with the increase in temperature, attaining its maximum value at the TC and then undergoing a jump, showing the presence of a second-order phase transition from the superconducting state to the normal state. Finally, the magnetization of both the itinerant and localized electrons decreases with the increase in temperature and finally becomes zero at TC = 1.6 K and magnetic phase transition temperature T = 2 K, respectively, which results in a magnetic phase transition from a ferromagnetic to a paramagnetic state. Our finding is in good agreement with the previous findings.

Keywords: spin triplet superconductivity, Green’s function, condensation energy, density of state, specific heat, magnetization

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Authors: Sara Kanzi, Izzet Sakalli

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The effect of Lorentz symmetry breaking (LSB) on the Hawking radiation of Schwarzschild-like black hole found in the bumblebee gravity model (SBHBGM) is studied in the framework of quantum gravity. To this end, we consider Hawking radiation spin-0 (bosons) and spin-12particles (fermions), which go in and out through the event horizon of the SBHBGM. We use the modified Klein-Gordon and Dirac equations, which are obtained from the generalized uncertainty principle (GUP) to show how Hawking radiation is affected by the GUP and LSB. In particular, we reveal that independent of the spin of the emitted particles, GUP causes a change in the Hawking temperature of the SBHBGM. Furthermore, we compute the semi-analytic greybody factors (for both bosons and fermions) of the SBHBGM. Thus, we reveal that LSB is effective on the greybody factor of the SBHBGM such that its redundancy decreases the value of the greybody factor. Our findings are graphically depicted.

Keywords: bumblebee gravity model, Hawking radiation, generalized uncertainty principle, Lorentz symmetry breaking

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Authors: Manuel Urueña Palomo

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In this paper, we introduce the study of a new solution to gravitational singularities by violating the energy conditions of the Penrose Hawking singularity theorems. We consider that a shift to negative energies, and thus, to negative masses, takes place at the event horizon of a black hole, justified by the original, singular and exact Schwarzschild solution. These negative energies are supported by relativistic particle physics considering the negative energy solutions of the Dirac equation, which states that a time transformation shifts to a negative energy particle. In either general relativity or full Newtonian mechanics, these negative masses are predicted to be repulsive. It is demonstrated that the model fits actual observations, and could possibly clarify the size of observed and unexplained supermassive black holes, when considering the inflation that would take place inside the event horizon where massive particles interact antigravitationally. An approximated solution of the model proposed could be simulated in order to compare it with these observations.

Keywords: black holes, CPT symmetry, negative mass, time transformation

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Authors: Danah S. Alabdulmohsin

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Due to the fast growth of organizational data as well as the emergence of new technologies such as artificial intelligence (AI), organizations tend to utilize these new technologies in their enterprise information systems (EIS) either to overcome the issues they struggle with or to enhance their functions. The aim of this paper is to review the potential role of AI technologies in EIS, namely: enterprise resource planning systems (ERP), customer relation management systems (CRM), supply chain management systems (SCM), knowledge systems (KM), and human resources management systems (HRM). The paper provided the definitions of these systems as well as the definitions of AI technologies that have been used in EIS. In addition, the paper discussed the challenges that organizations might face while integrating AI with their information systems and explained why some organizations fail in achieving successful implementations of the integration.

Keywords: artificial intelligence, AI, enterprise information system, EIS, integration

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Authors: Yang Xiaodong

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This article explores the application and structural characteristics of flexible and programmable systems in electronic systems, with a focus on analyzing their advantages and architectural differences in dealing with complex environments. By introducing mathematical models and simulation experiments, the performance of dynamic module combination in flexible systems and fixed path selection in programmable systems in resource utilization and performance optimization was demonstrated. This article also discusses the mutual transformation between the two in practical applications and proposes a solution to improve system flexibility and performance through dynamic reconfiguration technology. This study provides theoretical reference for the design and optimization of flexible and programmable systems.

Keywords: flexibility, programmable, electronic systems, system architecture

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Authors: Salisu Ibrahim

Abstract:

The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: David C. Ni

Abstract:

The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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Authors: Ryspek Usubamatov, Tan San Chin, Sarken Kapaeva

Abstract:

Productivity of the manufacturing systems depends on technological processes, a technical data of machines and a structure of systems. Technology is presented by the machining mode and data, a technical data presents reliability parameters and auxiliary time for discrete production processes. The term structure of manufacturing systems includes the number of serial and parallel production machines and links between them. Structures of manufacturing systems depend on the complexity of technological processes. Mathematical models of productivity rate for manufacturing systems are important attributes that enable to define best structure by criterion of a productivity rate. These models are important tool in evaluation of the economical efficiency for production systems.

Keywords: productivity, structure, manufacturing systems, structural design

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Authors: Elke Mackensen

Abstract:

Systems Engineering plays a key role during industrial product development of complex technical systems. The need for systems engineers in industry is growing. However, there is a gap between the industrial need and the academic education. Normally the academic education is focused on the domain specific design, implementation and testing of technical systems. Necessary systems engineering expertise like knowledge about requirements analysis, product cost estimation, management or social skills are poorly taught. Thus, there is the need of new academic concepts for teaching systems engineering skills. This paper presents a project-orientated training concept to prepare students from different technical degree programs for systems engineering activities. The training concept has been initially implemented and applied in the industrial engineering master program of the University of Applied Sciences Offenburg.

Keywords: educational systems engineering training, requirements analysis, system modelling, SysML

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Ana Hol

Abstract:

Digital systems are in the cognitive wave of the eTransformations and are now extensively aimed at meeting the individuals’ demands, both those of customers requiring services and those of service providers. It is also apparent that successful future systems will not just simply open doors to the traditional owners/users to offer and receive services such as Uber for example does today, but will in the future require more customized and cognitively enabled infrastructures that will be responsive to the system user’s needs. To be able to identify what is required for such systems, this research reviews the historical and the current effects of the eTransformation process by studying: 1. eTransitions of company websites and mobile applications, 2. Emergence of new sheared economy business models as Uber and, 3. New requirements for demand driven, cognitive systems capable of learning and just in time decision making. Based on the analysis, this study proposes a Cognitive eTransformation Framework capable of guiding implementations of new responsive and user aware systems.

Keywords: system implementations, AI supported systems, cognitive systems, eTransformation

Procedia PDF Downloads 241