Related papers: Handling the Cornell potential within the Lagrange…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow…
The method of path integral hadronization is applied to a local quark-diquark toy model in order to derive an effective chiral meson-baryon Lagrangian. Further generalizations to models including both scalar and axial-vector diquarks as…
Several applications of the moment method in random matrix theory, especially, to local eigenvalue statistics at the spectral edges, are surveyed, with emphasis on a modification of the method involving orthogonal polynomials.
A permanent challenge in physics and other disciplines is to solve partial differential equations, thereby a beneficial investigation is to continue searching for new procedures to do it. In this Letter, a novel Monte-Carlo Metropolis…
In this work, we incorporate long-range electrostatic interactions in the form of the Coulomb model with fixed charges into the functional form of short-range machine-learning interatomic potentials (MLIPs), particularly in the Moment…
We consider the finite element method on locally damaged meshes allowing for some distorted cells which are isolated from one another. In the case of the Poisson equation and piecewise linear Lagrange finite elements, we show that the usual…
We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field…
We present a unified framework for studying Coulomb interactions in arbitrary environments using macroscopic quantum electrodynamics on the basis of the electromagnetic Green's function. Our theory can be used to derive the Coulomb…
We propose to use the complex quantum dynamics of a massive particle in a non-quadratic potential to reconstruct an initial unknown motional quantum state. We theoretically show that the reconstruction can be efficiently done by measuring…
The variable-phase approach is applied to scattering and bound states in an attractive Coulomb potential, statically screened by a two-dimensional (2D) electron gas. A 2D formulation of Levinson's theorem is used for bound-state counting…
Coulomb gases are special probability distributions, related to potential theory, that appear at many places in pure and applied mathematics and physics. In these short expository notes, we focus on some models, ideas, and structures. We…
With the use of the stereographic projection of momentum space into the four-dimensional sphere of unit radius. the possibility of the analytical solution of the three-dimensional two-body Lippmann-Schwinger equation with the Coulomb…
I consider the behavior of the quark-antiquark potential, called the Cornell Potential, in a quark-gluon plasma. Since mesons are no longer bound in the quark-gluon plasma, there might be a relationship between the string tension of the…
Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the…
In the past few years a wealth of high quality data has made possible to test current theoretical ideas about the properties of hadrons subject to extreme conditions of density and temperature. The relativistic heavy-ion program carried out…
Over the past decade inter-atomic potentials based on machine-learning (ML) techniques have become an indispensable tool in the atomic-scale modeling of materials. Trained on energies and forces obtained from electronic-structure…
We describe a practical procedure to calculate the Coulomb matrix elements of 2D spatially separated and confined charge carriers, which are needed for detailed theoretical descriptions of important condensed matter finite systems. We…
Considering the Cornell potential $V(r)=-\frac{4\alpha_s}{3r}+br+c$, we have revisited the Dalgarno's method of perturbation by incorporating two scales $r^{short}$ and $r^{long}$ as integration limit so that the perturbative procedure can…
The development of smooth particle magnetohydrodynamic (SPMHD) has significantly improved the simulation of complex astrophysical processes. However, the preservation the solenoidality of the magnetic field is still a severe problem for the…