Related papers: Spin-Orbital Motion: Symmetry and Dynamics
Spatiotemporal vortex pulses (STVPs) are wavepackets that carry transverse orbital angular momentum (OAM), whose proper quantification has been the subject of recent debate. In this work, we introduce a simplified mechanical model of STVPs,…
In this article, we introduce a semi-orthogonal tribonacci wavelet and develop a semi-orthogonal tribonacci wavelet collocation method, offering an effective numerical method for solving a class of non-linear singular BVPs.
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
We explore conformal primary wavefunctions for all half integer spins up to the graviton. Half steps are related by supersymmetry, integer steps by the classical double copy. The main results are as follows: we 1) introduce a convenient…
This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…
The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in…
This thesis details an effort to generate astrophysically interesting solutions to the two-body problem in General Relativity. The thesis consists of two main parts. The first part presents an analytical variational principle for describing…
The exact equation of spin motion in a cylindrical coordinate system with allowance for electric dipole moments of particles has been derived. This equation is convenient for analytical calculations of spin dynamics in circular storage…
We present some applications of general harmonic/wavelet analysis approach (generalized coherent states, wavelet packets) to numerical/analytical calculations in (nonlinear) quasiclassical/quantum beam dynamics problems. (Naive) deformation…
We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free of a physical wavefunction, is presented…
Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on…
We study periodic orbits in a time-dependent two-center Stark-Zeeman system, which models the motion of a charged particle attracted by two fixed Coulomb centers and subject to external magnetic and time-dependent electric fields. A…
The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known…
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into $L^2(\mathbb{R}^d)$ basis functions in momentum-space to obtain a system of…
We study the classical dynamics of spinning particles using scattering amplitudes and eikonal exponentiation. We show that observables are determined by a simple algorithm. A wealth of complexity arises in perturbation theory as positions,…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…
We consider a variational approach to solve parabolic problems by minimising a functional over time and space. To achieve existence results we investigate the notion of $\mathscr{A}$-quasiconvexity for non-homogeneous operators in…