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The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…

We study the restricted motion of an electric charge in a spherical surface in the field of a magnetic dipole. This is the classical non-relativistic St\"oermer problem within a sphere, with the dipole in its centre. We start from a…

The Bertrand theorem concluded that; the Kepler potential, and the isotropic harmonic oscillator potential are the only systems under which all the orbits are closed. It was never stressed enough in the physical or mathematical literature…

It is proposed a Lagrangian for the quasi-rigid extended charged particle, which consists of a bare point particle term plus the standard electromagnetic minimal coupling. The quasi-rigid motion is imposed as a constraint. The extension of…

The Fermi acceleration model was introduced to describe how cosmic ray particles are accelerated to great speeds by interacting with moving magnetic fields. We identify a new variation of the model where light ions interact with a moving…

A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…

A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the…

We adopt the fixed node restricted path integral Monte Carlo method within the "Worm algorithm" to simulate Wigner's Jellium model at finite, non zero, temperatures using free-particle nodes of the density matrix. The new element is that we…

We demonstrate the polarization of electron orbital angular momentum (OAM) in neutral atoms by integrating the Zeeman effect with attosecond transient absorption spectroscopy (ATAS). Using density matrix simulations, we show that in a…

Machine-learning electronic Hamiltonians achieve orders-of-magnitude speedups over density-functional theory, yet current models omit long-range Coulomb interactions that govern physics in polar crystals and heterostructures. We derive…

We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these…

We show that the Einstein-Hilbert action for the gravitational field can be obtained as a linear low-energy approximation for the dynamical massless fields in the theory with the lagrangian quadratic in the gauge field strength-tensor of…

We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the…

We propose a method by which one could use modified antimatter gravity experiments in order to perform a high-precision test of antimatter charge neutrality. The proposal is based on the application of a strong, external, vertically…

The perturbations of the hyperbolic motion of a test particle due to the general relativistic gravitoelectromagnetic Schwarzschild and Lense-Thirring components of the gravitational field of a rotating massive body are analytically worked…

The frozen star is a recent proposal for a non-singular solution of Einstein's equations that describes an ultracompact object which closely resembles a black hole from an external perspective. The frozen star is also meant to be an…

The intrinsic magnetic fields of exoplanets affect the structure of their atmospheres and plasmaspheres and, therefore, the observational manifestations of transit absorptions. This work proposes a new method for constraining the presence…

Existing space-based cold atom experiments have demonstrated the utility of microgravity for improvements in observation times and for minimizing the expansion energy and rate of a freely evolving coherent matter wave. In this paper we…

Bernard [3] showed that a Ma\~n\'e generic convex Hamiltonian has only non-degenerate periodic orbits on a given energy level. We show that one can use this result to prove that for a generic potential the prime periodic orbits of fixed…

We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…