Article
Mathematics
Piero D'Ancona, Luca Fanelli, Nico Michele Schiavone
Summary: The study demonstrates the location of eigenvalues when perturbing the n-dimensional massive Dirac operator and potential V under certain conditions. For the massless case, it shows that the discrete spectrum is empty and identical to the spectrum of the unperturbed operator under specific smallness assumptions on V.
MATHEMATISCHE ANNALEN
(2022)
Article
Mathematics, Applied
Brice Flamencourt
Summary: In this paper, Dirac-like operators with piecewise constant mass terms on spin manifolds are considered, and the behavior of their spectra when the mass parameters become large is studied. In several asymptotic regimes, effective operators, including the extrinsic Dirac operator and a generalized MIT Bag Dirac operator, appear. This extends some previously known results for Euclidean spaces to the case of general spin manifolds.
JOURNAL OF GEOMETRY AND PHYSICS
(2022)
Article
Mathematics, Applied
Jicheng Zhang, Quanling Deng, Xin Li
Summary: This paper generalizes the C-0 stable generalized finite element methods (SGFEM) from its underlying C-0 finite element basis to isogeometric analysis (IGA) with Cp-1 B-spline basis. By applying a technique based on transformations between B splines and Bernstein-Bezier polynomials, the Cp-1 continuity requirement for enriched functions of arbitrary degree is met, while ensuring good conditioning when the underlying IGA space is linear or quadratic.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Multidisciplinary Sciences
Y. Chargui, K. Abdel-Rahman, F. Abdel-Ilah
Summary: This study examines the perturbation of the one-dimensional generalized relativistic harmonic oscillator by a Lorentz scalar delta-shaped interaction, revealing significant changes in the system's energy spectrum structure when a singular potential is present. An anomaly of doubly degenerate energy levels is observed as the strength of the local term approaches infinity. Energy eigenvalues within the range [-mc(2), mc(2)] are obtained for certain negative values of the delta-coupling and all settings of the oscillator parameters.
Article
Physics, Multidisciplinary
H. Hamdi, H. Benzair, M. Merad, T. Boudjedaa
Summary: The exact solution for the relativistic spinning particle in an inhomogeneous magnetic field is obtained in this study. It uses the path integral formalism to analytically eliminate the singularity at the point y = -1/a, which results in a dependent position mass for the kinetic term. By transforming the coordinates, the Green function and electron propagator are calculated, and the energy eigenvalues and corresponding eigenfunctions are extracted. The limit case is derived for a small parameter, and the thermodynamic properties are established.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
Shokhrukh Yu. Kholmatov, Saidakhmat N. Lakaev, Firdavsjon M. Almuratov
Summary: The study investigates the spectral properties of a Schrodinger-type operator associated with a one-particle system in one-dimensional or two-dimensional lattice. By analyzing the regularity of the Hopping matrix and decay of the potential, the existence and finiteness of eigenvalues of the operator are determined, with further examination on the asymptotics of eigenvalues as the parameter μ approaches 0.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Nanoscience & Nanotechnology
Wei Fu, Sha-Sha Ke, Ming-Xing Lu, Hai-Feng Lu
Summary: Research on the formation of bound states in tilted Dirac materials is important for understanding materials with Dirac cones. The study shows that tilting accelerates the process of atomic collapse, while overtilting leads to the disappearance of bound states.
PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES
(2021)
Article
Physics, Mathematical
Naiara Arrizabalaga, Albert Mas, Tomas Sanz-Perela, Luis Vega
Summary: In this article, we study the spectral properties of Dirac operators on bounded domains Omega subset of R-3 with boundary conditions of electrostatic and Lorentz scalar type, which depend on a parameter tau belonging to the set of real numbers. The case of tau = 0 corresponds to the MIT bag model. We demonstrate that the eigenvalues can be parameterized as increasing functions of tau and we use this monotonicity to investigate the limits as tau approaches positive or negative infinity. We prove that if Omega is not a ball, then the first positive eigenvalue is greater than the eigenvalue of a ball with the same volume for sufficiently large tau. Moreover, we show that the first positive eigenvalue converges to the mass of the particle as tau tends to negative infinity, and we also analyze its first order asymptotics.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
P. Rajesh Kumar
Summary: An improved and elegant quantum condition for the bound state problem in non-relativistic quantum mechanics is presented, using the Nikiforov-Uvarov functional analysis method. Two simple formulas are obtained to calculate the energy spectrum for the bound state problem, and the corresponding eigenstates are derived in terms of hypergeometric functions. Two bound state problems are studied using this improved quantum condition.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Chemistry, Physical
Luca Nanni
Summary: The theory of relativity is not covered in theoretical chemistry courses, but it plays a significant role in studying the electronic structure of heavy elements. The laws of relativity, initially deemed unusual for chemistry, provide fundamental tools for investigating the properties of heavy atoms. Chemists can learn to master this relatively unfamiliar subject by studying the electronic structure of heavy elements and becoming familiar with its elegant formalism.
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
(2023)
Review
Physics, Multidisciplinary
O. R. Smits, P. Indelicato, W. Nazarewicz, M. Piibeleht, P. Schwerdtfeger
Summary: This article reviews the progress in atomic structure theory, focusing on superheavy elements and their predicted ground state configurations that are important for determining an element's position in the periodic table. Understanding the electronic structure and correlations in the regime of large atomic numbers requires solving the Dirac equation accurately in strong Coulomb fields and considering quantum electrodynamic effects. The article specifically addresses the challenges associated with dealing with the many-particle Dirac equation and discusses the future possibility of conducting many-electron atomic structure calculations beyond a critical nuclear charge. The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
G. Gaigalas, D. Kato
Summary: The latest version of the grasp2018 package extends the multiconfigurational Dirac-Hartree-Fock method to account for crystal field effects in complex systems. Instead of using simplified treatments, this program uses a fully ab-initio method to handle crystal field effects, with examples provided in the source directory for CF_Hamiltonian program usage.
COMPUTER PHYSICS COMMUNICATIONS
(2021)
Article
Mathematics, Applied
Hayato Chiba, Masahiro Ikeda, Isao Ishikawa
Summary: The generalized spectral theory is an effective method for analyzing the continuous spectrum of a linear operator. It calculates the generalized spectrum by using analytic continuations and the construction of resolvent operators. This paper studies the generalized spectra of Perron-Frobenius operators and one-sided/two-sided shifts of finite type, as well as proposes a new construction method for the Gelfand triplet of symbolic dynamical systems. Additionally, an asymptotic formula for the iteration of Perron-Frobenius operators is provided.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2023)
Article
Physics, Multidisciplinary
I. J. Njoku, C. P. Onyenegecha, C. J. Okereke, E. Omugbe
Summary: In this paper, the analytical solutions of the Dirac equation in the presence of external fields are presented using the formula method with the pseudoharmonic potential. The exact spin symmetry and pseudospin symmetry cases are examined, and the non-relativistic energies are obtained using a mapping to the non-relativistic limit. The results are consistent with the literature with slight variations arising from methodology and the conversion factors used.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
Hua Chen, Hong-Ge Chen, Jin-Ning Li
Summary: By studying selfadjoint Hormander operators on non-equiregular sub-Riemannian manifolds, we have successfully established upper bounds for eigenvalues that depend on the volume of the subunit ball and the measure of the manifold. Under certain conditions, we have obtained explicit upper bounds for eigenvalues which exhibit polynomial growth in k with an optimal order related to the non-isotropic dimension of the manifold.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2022)
Article
Computer Science, Interdisciplinary Applications
Usman Riaz, E. Seegyoung Seol, Robert Hager, Mark S. Shephard
Summary: The accurate representation and effective discretization of a problem domain into a mesh are crucial for achieving high-quality simulation results and computational efficiency. This work presents recent developments in extending an automated tokamak modeling and meshing infrastructure to better support the near flux field following meshing requirements of the XGC Gyro-kinetic Code.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Zhenglu Li, Gabriel Antonius, Yang-Hao Chan, Steven G. Louie
Summary: This article presents a workflow for practical calculations of electron-phonon coupling and includes the effect of many-electron correlations using GW perturbation theory. The workflow combines different software packages to enable accurate calculations at the level of quasiparticle band structures.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Akihiro Koide, Sara Rabouli, Pierre Le Meur, Sylvain Tricot, Philippe Schieffer, Didier Sebilleau, Calogero R. Natoli
Summary: We present the MsSpec Atomic Scattering Amplitude Package (MASAP), which includes a computation program and a graphical interface for generating atomic scattering amplitude (ASA). The study investigates the applicability of plane wave (PW) and curved spherical wave (SW) scattering in describing electron propagation. The results show that the imaginary part of the optical potential enhances the elastic scattering in the forward direction but causes damping effects in other directions.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
A. Bagci, Gustavo A. Aucar
Summary: The electron repulsion integrals over Slater-type orbitals with non-integer principal quantum numbers are investigated in this study. These integrals are important in calculations of many-electron systems. New relationships free from hyper-geometric functions are derived to simplify the calculations. With the use of auxiliary functions and straightforward recurrence relationships, these integrals can be efficiently computed, providing initial conditions for the evaluation of expectation values and potentials.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrzej Daniluk
Summary: RHEED_DIFF_2D is an open-source software for qualitative numerical simulations of RHEED oscillation intensity changes with layer deposition, used for interpreting heteroepitaxial structures under different scattering crystal potential models.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Niklas Kuehl, Hendrik Fischer, Michael Hinze, Thomas Rung
Summary: The article presents a strategy and algorithm for simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The proposed method improves computational efficiency by introducing a bunch matrix, resulting in higher accuracy and practical applicability.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jose M. Rodriguez-Borbon, Xian Wang, Adrian P. Dieguez, Khaled Z. Ibrahim, Bryan M. Wong
Summary: This paper presents an open-source software package called TRAVOLTA for massively parallelized quantum optimal control calculations on GPUs. The TRAVOLTA package is an improvement on the previous NIC-CAGE algorithm and incorporates algorithmic improvements for faster convergence. Three different variants of GPU parallelization are examined to evaluate their performance in constructing optimal control fields in various quantum systems. The benchmarks show that the GPU-enhanced TRAVOLTA code produces the same results as previous CPU-based algorithms but with a speedup of more than ten times. The GPU enhancements and algorithmic improvements allow large quantum optimal control calculations to be efficiently executed on modern multi-core computational hardware.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Weijie Hua
Summary: This work introduces a program called MCNOX for computing and analyzing ultrafast nonlinear X-ray spectra. It is designed for cutting-edge applications in photochemistry/photophysics enabled by X-ray free-electron lasers and high harmonic generation light sources. The program can calculate steady-state X-ray absorption spectroscopy and three types of ultrafast nonlinear X-ray spectra, and it is capable of identifying major electronic transitions and providing physical and chemical insights from complex signals.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Leandro Benatto, Omar Mesquita, Lucimara S. Roman, Rodrigo B. Capaz, Graziani Candiotto, Marlus Koehler
Summary: Photoluminescence Quenching Simulator (PLQ-Sim) is a user-friendly software for studying the dynamics of photoexcited states at the interface between organic semiconductors. It provides important information on organic photovoltaic and photothermal devices and calculates transfer rates and quenching efficiency.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Dongming Li, James Kestyn, Eric Polizzi
Summary: This study introduces a practical and efficient approach to calculate the all-electron full potential band structure in real space using a finite element basis. Instead of the k-space method, this method solves the Kohn-Sham equation self-consistently within a larger finite system enclosing the unit-cell. Non-self-consistent calculations are then performed in the Brillouin zone to obtain the band structure results, which are found to be in excellent agreement with the pseudopotential k-space method. Furthermore, the study successfully observes the band bending of core electrons.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
R. Kleiber, M. Borchardt, R. Hatzky, A. Koenies, H. Leyh, A. Mishchenko, J. Riemann, C. Slaby, J. M. Garcia-Regana, E. Sanchez, M. Cole
Summary: This paper describes the current state of the EUTERPE code, focusing on the implemented models and their numerical implementation. The code is capable of solving the multi-species electromagnetic gyrokinetic equations in a three-dimensional domain. It utilizes noise reduction techniques and grid resolution transformation for efficient computation. Additionally, various hybrid models are implemented for comparison and the study of plasma-particle interactions. The code is parallelized for high scalability on multiple CPUs.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Pengliang Yang
Summary: This paper presents an open source software called SMIwiz, which combines seismic modelling, reverse time migration, and full waveform inversion into a unified computer implementation. SMIwiz supports both 2D and 3D simulations and provides various computational recipes for efficient calculation. Its independent processing and batchwise job scheduling ensure scalability, and its viability is demonstrated through applications on benchmark models.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Christian Tantardini, Miroslav Ilias, Matteo Giantomassi, Alexander G. Kvashnin, Valeria Pershina, Xavier Gonze
Summary: Material discovery has been an active research field, and this study focuses on developing pseudopotentials for actinides and super-heavy elements. These pseudopotentials are crucial for accurate first-principles calculations and simulations.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
S. Blanes, F. Casas, C. Gonzalez, M. Thalhammer
Summary: This paper explores the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. Numerical experiments confirm the advantages of the proposed fourth-order modified operator splitting method over traditional splitting methods in dealing with Gross-Pitaevskii systems.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Siegfried Kaidisch, Thomas U. Hilger, Andreas Krassnigg, Wolfgang Lucha
Summary: Motivated by a use case in theoretical hadron physics, this paper revisits an application of a pole-sum fit to dressing functions of a confined quark propagator. Specifically, it investigates approaches to determine the number and positions of singularities closest to the origin for a function known numerically on a specific grid on the positive real axis. Comparing the efficiency of standard techniques to a pure artificial-neural-network approach and a combination of both, it finds that the combined approach is more efficient. This approach can be applied to similar situations where the positions of poles need to be estimated quickly and reliably from real-axis information alone.
COMPUTER PHYSICS COMMUNICATIONS
(2024)