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We review the recent development of machine-learning (ML) force-field frameworks for Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets, focusing on the general theory and implementations of symmetry-invariant…
This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent…
We study the low-frequency behavior of the {\it ac} conductivity $\sigma(\omega)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|\omega|$ correction…
The asymptotic behaviour of the electromagnetic form factors of the electron and quark is obtained in the double-logarithmic approximation for Sudakov kinematics, i.e. for the case that the value of the momentum transfer is much greater…
The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. It allows to control contribution from each scale of underlying…
We present a review of our recent work in extending the successful dynamical mean-field theory from the equilibrium case to nonequilibrium cases. In particular, we focus on the problem of turning on a spatially uniform, but possibly time…
The mean field type approach based on the self-consistent consideration of an effective field created by electron transfer is developed for a description of thermodynamics of the Hubbard type models with an infinitely large on-site…
A new model of nonlinear electrodynamics named as \emph{"double-logarithmic"} is introduced and investigated. The theory carries one dimensionful parameter of the $\beta$ as Born-Infeld electrodynamics. It is shown that the dual symmetry…
An approximate analytical scheme of the dynamical mean field theory (DMFT) is developed for the description of the electron (ion) lattice systems with Hubbard correlations within the asymmetric Hubbard model where the chemical potentials…
Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this…
We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…
We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or…
Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these…
The field line random walk (FLRW) of magnetic turbulence is one of the important topics in plasma physics and astrophysics. In this article by using the field line tracing method mean square displacements (MSD) of FLRW is calculated in all…
One considers the quantum dynamics of a charged spin-1/2 particle in an extended external eletromagnetic field that arises from the reduction of a 5-dimensional Abelian gauge theory. The non-relativistic regime of the reduced 4D-dynamics is…
The study of the Brownian motion of a charged particle in electric and magnetic fields fields has many important applications in plasma and heavy ions physics, as well as in astrophysics. In the present paper we consider the electromagnetic…
Upcoming experiments on the interaction of electrons with intense laser fields are envisaged to become more and more accurate, which calls for theoretical computations of rates and probabilities with correspondingly higher precision. In…
A new class of analytic and parameter-free, strongly correlated wave functions of simple functional form is derived for few electrons in two-dimensional quantum dots under high magnetic fields. These wave functions are constructed through…
Electromagnetic fields of an accelerated charge are derived from the first principles using Coulomb's law and the relativistic transformations. The electric and magnetic fields are derived first for an instantaneous rest frame of the…
We study the problem of two particles with Coulomb repulsion in a two-dimensional disordered potential in the presence of a magnetic field. For the regime, when without interaction all states are well localized, it is shown that above a…