Related papers: Generalizations of MICZ-Kepler system
We introduce the notion of multiplication kernels of birational and $D$-module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its…
We formulate and approximately solve a specific many-body generalization of the Landau-Zener problem. Unlike with the single particle Landau-Zener problem, our system does not abide in the adiabatic ground state, even at very slow driving…
A system of generalized kinetic equations for the distribution functions of two-dimensional Dirac fermions scattered by impurities is derived in the Born approximation with respect to short-range impurity potential. It is proven that the…
In this paper we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as…
We consider a $N$-particle interacting particle system with the vision geometrical constraints and reflected noises, proposed as a model for collective behavior of individuals. We rigorously derive a continuity-type of mean-field equation…
We investigate the dielectrophoretic motion of charge-neutral, polarizable nanocolloids through molecular dynamics simulations. Comparison to analytical results derived for continuum systems shows that the discrete charge distributions on…
A rigorous definition of a path integral for a spinning particle in three dimensions is given on a regular cubic lattice. The critical diffusion constant and the associated critical exponents in each spin are calculated. Continuum field…
We derive the perihelion precession of planetary orbits using quantum field theory extending the Standard Model to include gravity. Modeling the gravitational bound state of an electron via the Dirac equation of unified gravity [Rep. Prog.…
In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for…
The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for…
Classical mechanical treatment of charged particle beam optics is so far very satisfactory from a practical point of view in applications ranging from electron microscopy to accelerator technology. However, it is desirable to understand the…
The Keller-Segel model is a system of partial differential equations that describes the movement of cells or organisms in response to chemical signals, a phenomenon known as chemotaxis. In this study, we analyze a doubly parabolic…
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
We consider integrable spherical analogue of the Darboux potential, which appear in the problem (and its generalizations) of the planar motion of a particle in the field of two and four fixed Newtonian centers. The obtained results can be…
Periodically driven dynamics of a particle moving in the field Coulomb plus confining potential is treated for one and three dimensional cases. Critical value of the external field strength at which chaotization will occur is evaluated…
We propose a general construction of quantum states for linear canonical quantum fields on a manifold, which encompasses and generalizes the "standard" procedures existing in textbooks. Our method provides pure and mixed states on the same…
We analyze the diffraction of elementary systems as the electron by light gratings when they are described by charge distributions instead of the usual point-like form. The treatment of the problem is based on the introduction, in analogy…
We discuss the general formalism for the calculation in light-cone quark models of the fully unintegrated, off-diagonal quark-quark correlator of the nucleon. The corresponding distributions in impact parameter space are the Wigner or…
Point-particle dynamics is reformulated as a field theory. This is achieved by using the unfolded dynamics approach that makes it possible to give dynamical interpretation to the concept of physical dimension which is 1 for a point particle…
The details of trajectories of charged particles become increasingly important for proper understanding of processes of formation of radiation in strong and curved magnetic fields. Because of damping of the perpendicular component of…