0000000000923424
AUTHOR
Souraya Goumri-said
Analytical investigation of solitary waves in nonlinear Kerr medium
Abstract We study analytically the solution of nonlinear equation which result from the propagation of electromagnetic waves within a nonlinear Kerr medium. The medium is characterized by a dielectric constant which varies periodically and depends on the local field intensity. As a first step, we detail the resolution of the nonlinear equations with a quadratic nonlinearity. After that, we apply the slowly varying envelope approximation to obtain a Sine–Gordon equation. In this kind of nonlinearity, a gap solitons occurs. Moreover we verify that the solutions of the nonlinear equation for all frequencies within the gap are solitons solutions. After that we study the conditions of apparition…
Electronic momentum distribution in the one-dimensional extended Hubbard model: determinantal Monte Carlo study
Abstract The effect of electron–electron (e–e) interaction on trans -polyacetylene ( t -PA) properties is investigated within the framework of an extended Hubbard model in one dimension. For numerical calculation, we use the determinantal version of quantum Monte Carlo approach, which provides a breakthrough to simulate statistical fluctuations in the systems with many degrees of freedom, in order to obtain mean values for observables of physical interest. This allows one to analyze the discrete system of fermions without encountering the numerical instabilities that generally occur from the original problem involving anticommuting fermion operators. We calculate the electronic momentum dis…
Numerical study of photolithography system: electromagnetic differential method
The R-matrix propagation algorithm is incorporated into the differential method to achieve an extended capability for modelling a photolithography systems. We show throughout this work the ability of the R-matrix algorithm and differential method to analyse gratings of arbitrary depth, profile, and conductivity without encountering numerical instabilities. We calculate the field intensity and the transmitted amplitudes in the 0 and −1 orders below different masks. We study also the influence of the various parameters (incidence, groove spacing, groove depth and index of refraction) on the field intensity maps and the transmittivity power. These results agree with the experimental patent: we…
Quantum Monte Carlo study of insulating state in NaV2O5
Abstract Quantum Monte Carlo (QMC) methods are being increasingly used as complements to Hartree–Fock (HF) methods for computing the electronic structure of molecules and materials. We investigate the nature of the insulating state driven by electronic correlations in the ladder compound NaV 2 O 5 ; considered as a quarter-filled system. We use an extended Hubbard model (EHM) to study the role of on-site and inter-site Coulomb interaction. It is found that the insulating state in the charge-disordered phase of this compound take origin from the transfer of spectral density and dynamical fluctuations. Our calculation allows us also, to understand the origin of the insulating states above T C…
Zinc-blende AlN and GaN under pressure: structural, electronic, elastic and piezoelectric properties
In this paper we report a theoretical study of the structural, elastic, electronic and piezoelectric properties of zinc-blende AlN and GaN under the pressure effect. The study is focused on the first-principles all electron full-potential augmented plane wave plus local orbitals calculations within the density-functional theory. The results of bulk properties, including lattice constants, bulk modulus and derivatives and band structures are obtained and compared using both the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation functional. We find that the GGA does not give a significant improvement over LDA. We also report calcula…
New quantum Monte Carlo formulation for modeling trans-polyacetylene properties: specific heat calculation
Abstract In this paper we propose a new hybridization scheme for numerical simulation based on the determinantal quantum Monte Carlo and analytical model to treat the vibration mode of one-dimensional trans -polyacetylene chain. We use both of the extended Hubbard model (EHM) and Peierls–Hubbard model to compute the specific heat for different assumptions. For both the two models, our results indicate that the behavior of the specific heat is characterized by a maximum. We also introduce the effect of dimerization through Peierls–Hubbard model. In this case it is found that the specific heat magnitude is slightly more important when compared to specific heat value found with the EHM case. M…
Numerical simulations of photon scanning tunneling microscopy: role of a probe tip geometry in image formation
Abstract Numerical simulations of two-dimensional probe–object system emulating a photon scanning tunnelling microscope are presented. R -matrix propagation algorithm incorporated into the differential method was used to achieve an extended capability to rigorously model a realistic system consisting of both a probe and a sample. Influence of the probe tip parameters on image formation in scanning near-field microscopy has been investigated. Coupling of the near-field to a single-mode probe and formation of a guided fundamental mode in a probe were investigated for various probe widths and lengths. The influence of the probe taper shape and apex size on near-field images was studied for sin…
The behavior of correlation functions in trans-polyacetylene: quantum Monte Carlo study
We present results of a quantum Monte Carlo simulation of the one-dimensional half-filled Hubbard model to study different correlation functions in the trans-polyacetylene (t-PA) polymer. Magnetic structure of the model in t-PA is studied for a different range values of the Hubbard repulsion interactions, U and V ,w here U 4t , with V ∈[ U/2 ,U ] (t is the hopping matrix elements). In this work, we investigate the behavior of the magnetic correlation functions for different phases transitions between different ordering (antiferromagnetic and ferromagnetic) by varying the nearest-neighbor interactions U and V between different atomic sites. Our results indicate that there is a presence of a …
Prediction of structural and thermodynamic properties of zinc-blende AlN: molecular dynamics simulation
Abstract Structural and elastic properties of AlN are investigated by using a molecular dynamics simulation based on the Tersoff empirical interatomic potential. Both of zinc-blende and rock-salt structures are discussed. The calculated bulk properties and elastic constants agree well with the available experimental and theoretical data. The Thermodynamic properties in zinc-blende structure are also predicted including the Debye temperature, melting temperature, heat capacity, linear thermal coefficient. This study is helpful to understand the bahviour of physical properties of AlN when the temperature varies.
Quantum Monte-Carlo calculation of correlation functions of undistorted, cis-distorted and trans-distorted polyacene
Abstract We have studied polyacene within the Hubbard model to explore the effect of electrons correlations on the bond–bond correlation as well as spin–spin correlation functions. We employ the determinantal quantum Monte-Carlo to resolve the microscopic Hamiltonian of this system which involves a nearest-neighbor electron hopping matrix element t , an on-site Coulomb repulsion U . The objective of this study is to understand the effect of electron–electron (e–e) correlations on the structural instability in polyacene. We find strong similarities between polyacene and polyacetylene. The system shows no tendency to destroy the imposed bond-alternation pattern. The spin–spin correlations sho…
Theoretical study of an absorbing sample in infrared near-field spectromicroscopy
Abstract This paper is devoted to study the near-field spectrometry in the infrared spectral range. To understand the behavior of the infrared light diffracted by an object, numerical calculations have been carried out with Fourier Modale (FM) method within R-matrix algorithm. We consider the case of three-dimensional system including a translational symmetry in one direction, where is included an homogenous layer in which is buried an absorbing object. Using an optical near-field analysis and by calculating the electric field intensity distribution, both of the thickness effect and the lateral size of the absorbing sample are investigated. It is found that the distribution of the intensity…
Contribution à l'étude de la formation des images optiques en microscopie champ proche optique: effet de la sonde en deux dimensions
This work consists in the development of a theoretical tool for the purpose to undertake numerical simulations able to take into account the coupling between the probe and the object. The first part, concerns the combination of the differential method and the algorithms T and S, to overcome numerical problems which appear in the cases where the size of system (probe - object) is more realistic. The developed global model is two-dimensional and applied in polarization TE under the normal diffraction condition. We have used the developed model to study the formation of optical image by monomodes and multimodes probes. The obtained optical images at constant height, have allowed us to study th…
Empirical molecular dynamics study of structural, elastic and thermodynamic properties of zinc-blende-like SiGe compound
Abstract A three-body potential coupled with a molecular-dynamics method is used to calculate structural and thermodynamic properties of the hypothetical IV–IV compound SiGe in zinc-blende phase. A good agreement between the calculated and theoretical values of the lattice constant, the bulk modulus and its derivative, and the cohesive energy is obtained. We also compute the elastic constants, Debye temperature, lattice thermal expansion, and the specific heat. We investigate also, the structural properties of SiGe when rock-salt phase appears.
Quantum Monte Carlo study of the alternating extended Peierls–Hubbard model applied to the trans-polyacetylene
Abstract The one-dimensional alternating Peierls–Hubbard model is especially interesting as nontrivial model for conjugated polymer chains, such as polyacetylene. We study this model for chains of 64 sites using the determinantal method based on Hubbard–Stratonovich transformation. We obtain the first electronic energies and their mean fluctuations at half-filling as a function of the on-site electron–electron interaction (both short and long range U, V coupling are considered). We also study the effect of the electron–electron interaction on the dimerization by investigating some of the important correlation functions, such as spin–spin correlation, on-site charge and the specific heat. Th…