Related papers: Orbitron. Part II. Magnetic levitation
In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic…
The planar motion of a testing body in the field of gravity of the massive ring is studied. The "perihelion" precession due to non-relativistic reasons is demonstrated on this simple example of planar motion in the radially symmetric (in…
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…
The second post-Newtonian solution for the quasi-Keplerian motion of a test particle in the gravitational field of regular Bardeen black hole is derived. The solution is formulated in terms of the test particle's orbital energy and angular…
We construct a semiclassical theory for electrons in a non-Hermitian periodic system subject to perturbations varying slowly in space and time. We derive the energy of the wavepacket to first order in the gradients of the perturbations.…
The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on conservation of the adiabatic invariant, magnetic moment.…
We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…
A novel unitary transformation of the Hamiltonian that allows one to partially separate the center-of-mass motion for charged electron-hole systems in a magnetic field is presented. The two-mode squeezed oscillator states that appear at the…
The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on…
y formally diagonalizing with accuracy $\hbar$ the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase…
Some relevant transport properties of solids do not depend only on the spectrum of the electronic Hamiltonian, but on finer properties preserved only by unitary equivalence, the most striking example being the conductance. When interested…
It is shown that the motion of a multielectron atom in an external gravitational field in a good approximation is described by system of the Mathisson-Papapetrou equations, if we put as a classical angular momentum of the atom the…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
Like orbitals in atoms and molecules, persistent currents may appear in larger aggregates. Though classically, equilibrium magnetic moment of non-rotating objects is forbidden, it is known that equilibrium quantum circulating currents are…
We derive the rate of change of the mean motion up to the second post-Newtonian order for inspiralling compact binaries with spin, mass quadrupole and magnetic dipole moments on eccentric orbits. We give this result in terms of orbital…
The influence of an externally applied magnetic field upon classic cubic quintic dissipative solitons is investigated using both exact simulations and a Lagrangian technique. The basic approach is to use a spatially inhomogeneous magnetic…
We prove that either there exists at least one hamilton periodic orbit in a given energy close smooth hypersurface or there exist at least two hamilton periodic orbits in a near-by energy close smooth hypersurface. More general results also…
A many body Hamiltonian comprising pairing, quadrupole-quadrupole and spin-spin interaction is treated within a projected spherical basis with the aim of describing the detailed structure of the magnetic states of orbital and spin-flip…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be…