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Exploring novel solitary wave phenomena in Klein-Gordon equation using model expansion method.
Sci Rep
January 2025
Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, 71491, Tabuk, Saudi Arabia.
In this study, the -model expansion method is showed to be useful for finding solitary wave solutions to the Klein-Gordon (KG) equation. We develop a variety of solutions, including Jacobi elliptic functions, hyperbolic forms, and trigonometric forms, so greatly enhancing the range of exact solutions attainable. The 2D, 3D, and contour plots clearly show different types of solitary waves, like bright, dark, singular, and periodic solitons.
View Article and Find Full Text PDFRelativistic EELS scattering cross-sections for microanalysis based on Dirac solutions.
Ultramicroscopy
March 2025
Department of Materials, University of Oxford, 16 Parks Road, Oxford OX1 3PH, United Kingdom. Electronic address:
The rich information of electron energy-loss spectroscopy (EELS) comes from the complex inelastic scattering process whereby fast electrons transfer energy and momentum to atoms, exciting bound electrons from their ground states to higher unoccupied states. To quantify EELS, the common practice is to compare the cross-sections integrated within an energy window or fit the observed spectrum with theoretical differential cross-sections calculated from a generalized oscillator strength (GOS) database with experimental parameters. The previous Hartree-Fock-based and DFT-based GOS are calculated from Schrödinger's solution of atomic orbitals, which does not include the full relativistic effects.
View Article and Find Full Text PDFB-Spline Solution of the Two-Center Dirac Equation in the Electronic Continuum for Relativistic Molecular Photoionization.
J Chem Theory Comput
December 2024
Departamento de Química, Universidad Autónoma de Madrid, 28049 Madrid, Spain.
In this work, the two-center Dirac equation is solved numerically using an extension of an adapted B-spline basis set method previously implemented in relativistic atomic calculations (Fischer, C. F.; Zatsarinny, O.
View Article and Find Full Text PDFNon-Equilibrium Quantum Brain Dynamics: Water Coupled with Phonons and Photons.
Entropy (Basel)
November 2024
Dipartimento di Ingegneria Meccanica e Aerospaziale, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy.
We investigate Quantum Electrodynamics (QED) of water coupled with sound and light, namely Quantum Brain Dynamics (QBD) of water, phonons and photons. We provide phonon degrees of freedom as additional quanta in the framework of QBD in this paper. We begin with the Lagrangian density QED with non-relativistic charged bosons, photons and phonons, and derive time-evolution equations of coherent fields and Kadanoff-Baym (KB) equations for incoherent particles.
View Article and Find Full Text PDFPropagation Speeds of Relativistic Conformal Particles from a Generalized Relaxation Time Approximation.
Entropy (Basel)
October 2024
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Ciudad de Buenos Aires CP 1428, Argentina.
The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a generalized relaxation time approximation (RTA) where the relaxation time depends on the energy of the particles involved. We seek a solution of the kinetic equation by assuming a parameterized one-particle distribution function (1-pdf) which generalizes the Chapman-Enskog (Ch-En) solution to the RTA.
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