Related papers: A variational approach to time-dependent planar tw…
In this article, we study spatial Stark-Zeeman systems which describe the dynamics of a charged particle moving in three-dimensional space under the influence of a Coulomb potential, a magnetic field, and an electric field, possibly…
Time-dependent Stark-Zeeman systems describe the motion of an electron attracted by a proton subject to a magnetic and a time-dependent electric field. For instance the study of the dynamics of a gateway around the moon which is subject to…
We adapt the formally-defined Fokker action into a variational principle for the electromagnetic two-body problem. We introduce properly defined boundary conditions to construct a Poincare-invariant-action-functional of a finite orbital…
We apply Arnold's theory of generic smooth plane curves to Stark-Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many…
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…
We study the classical planar two-center problem of a particle $m$ subjected to harmonic-like interactions with two fixed centers. For convenient values of the dimensionless parameter of this problem we use the averaging theory for showing…
In this paper, we introduce the notion of planar two-center Stark- Zeeman systems and define four J+-like invariants for their periodic orbits. The construction is based on a previous construction for planar one-center Stark-Zeeman system…
We consider a motion of a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around…
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane,…
We consider a charged particle which is driven by a time-dependent flux threading a circular ring system. Various approaches including classical treatment, Fourier expansion method, time-evolution method, and Lewis-Riesenfeld method are…
We propose a new formulation of time-dependent coupled cluster with adaptive basis functions and division of the one-particle space into active and secondary subspaces. The formalism is fully bivariational in the sense of a real-valued…
We consider the problem of damping a control system with delay, described by first-order functional-differential equations on a temporal star graph. The delay in the system is time-proportional and propagates through the internal vertex. We…
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…
We consider a system consisting of one conservation law and one balance law with a time-dependent source term, and provide a comprehensive analysis of Riemann solutions, including the non-classical overcompressive delta shocks. The minimal…
We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover a function from given observations where the function or the data depend on time.…
A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…
We study numerically the dynamical system of a two-electron atom with the Darwin interaction as a model to investigate scale-dependent effects of the relativistic action-at-a-distance electrodynamics. This dynamical system consists of a…