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This is the second of two papers devoted to tight-binding electronic spectra on graphs with the topology of the sphere. We investigate the problem of an electron subject to a spin-orbit interaction generated by the radial electric field of…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
We formulate an inverse problem for an uncoupled space-time fractional Schr\"odinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the…
It has long been conjectured that generic dynamical systems has finite periodic orbits, ever since the time of Poincar\'e. In this article, a perturbation method is proposed for the $C^r$ closing of periodic orbits. This method is…
The wave-driven rotating torus (WDRT) is a recently proposed fusion concept where the rotational transform is provided by the E x B drift resulting from a minor radial electric field. This field can be produced, for instance, by the…
The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in $\Omega \neq 1$ and $\Lambda \neq 0$ {}Friedmann-Lema\^{\i}tre models. I explicitly write the second-order theories in terms of closed…
We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The…
Using the spinning worldline quantum field theory formalism we calculate the quadratic-in-spin momentum impulse $\Delta p_i^\mu$ and spin kick $\Delta a_i^\mu$ from a scattering of two arbitrarily oriented spinning massive bodies (black…
In light beams with circular or elliptic polarization, the transverse energy flow consists of the "spin" and "orbital" parts. Both of them can induce the orbital motion of microparticles suspended within the field of a light beam, and this…
In this paper, the isolated horizons with rotation are considered. It is shown that the symplectic form is the same as that in the nonrotating case. As a result, the boundary degrees of freedom can be also described by an SO$(1,1)$ BF…
Bertrand's theorem asserts that any spherically symmetric natural Hamiltonian system in Euclidean 3-space which possesses stable circular orbits and whose bounded trajectories are all periodic is either a harmonic oscillator or a Kepler…
The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We…
In gauge theories with an extended Higgs sector the classical equations of motion can have solutions that describe stable, closed finite energy vortices. Such vortices separate two disjoint Higgs vacua, with one of the vacua embedded in the…
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…
We study the motion of self deforming bodies with non zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame,…
The spinning electromagnetic universe, known also as the Rotating Bertotti-Robinson(RBR) spacetime is considered as a model to represent our cosmos. The model derives from different physical considerations, such as colliding waves, throat…
The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…
The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…
We find classical open string solutions in the $AdS_5\times S^5/\Zop_2$ orientifold with angular momenta along the five-sphere. The energy of these solutions has an expansion in integral powers of $\lambda$ with sigma-model corrections…
We formulate an analogue transverse first law for general closed marginally trapped surfaces in arbitrary spacetimes. The construction is intrinsically quasi-local and is attached directly to an individual marginally trapped surface, rather…