Related papers: Nonlinear realizations, the orbit method and Kohn'…
In analogy to the harmonic analysis for the Poincar\'e group with its irreducible representations characterizing free particles, the harmonic analysis for a nonlinear spacetime model as homogenous space of the extended Lorentz group GL(C^2)…
As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by…
Using the canonical Arnowitt-Deser-Misner Hamiltonian formalism, a "first law of mechanics" is established for binary systems of point masses moving along generic stable bound (eccentric) orbits. This relationship is checked to hold within…
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits…
A description of non-collinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective…
Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…
Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schrodinger equations in dimensions $n\neq 1$. Both focusing and defocusing cases of a power nonlinearity are considered,…
An analysis of single-electron orbits in combined coaxial wiggler and axial guide magnetic fields is presented. Solutions of the equations of motion are developed in a form convenient for computing orbital velocity components and…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
The main topic of this work concerns the formulation of the equations of motion and the consequent energy balance that they imply for this type of systems, In particular, the analytical development that we will carry out on the equations of…
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…
We complete the classification of isometric cohomogeneity-one actions on all symmetric spaces of noncompact type up to orbit equivalence.
Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables.…
The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal of this work is to discuss advantages and…
Two Fokker actions and corresponding equations of motion are obtained for two point particles in a post-Minkowski framework, in which the field of each particle is given by the half-retarded + half-advanced solution to the linearized…
We describe a geometrical method for tracing a planet's orbit using its velocity hodograph, that is, the path of the planet's velocity. The method requires only a straight edge, a compass, and the help of the hodograph. We also obtain…
Polaritons are the collective excitations of many atoms dressed by resonant photons, which can be used to explain the slow light propagation with the mechanism of electromagnetically induced transparency. As quasi-particles, these…
The Cosserat equations for equilibrium are derived by starting from the action of the group of smooth functions with values in the Lie group of rigid spatial motions on rigid frames in Euclidian space. The method of virtual work is…
An open question in the field of non-equilibrium statistical physics is whether there exists a unique way through which non-equilibrium systems equilibrate irrespective of how far they are away from equilibrium. To answer this question we…
We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.