Related papers: Classical Oscilators in General Relativity
We clarify the properties of the behavior of classical cosmological perturbations when the Universe experiences a bounce. This is done in the simplest possible case for which gravity is described by general relativity and the matter content…
A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $\omega^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $\omega^2(t)>0$…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of…
A generalization of the notion of ellipsoids to curved Riemannian spaces is given and the possibility to use it in describing the shapes of rotating bodies in general relativity is examined. As an illustrative example, stationary,…
This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the…
The forms of the generalized quantities that we have recently introduced are dependent on the phase of the probability amplitudes for spin-projection measurements. In this paper, we show explicitly that changing the phase gives different…
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
A classic harmonic oscillator model is developed to investigate the optical properties of coupled metal nanoparticles (MNPs) with arbitrary configuration in plane. The coupling coefficients are derived from classical electrodynamics. Using…
In the present paper we give conclusive arguments pointing at physical equivalence among conformally related metrics. Based on the argument that any consistent effective theory of spacetime must be invariant under the one-parameter group of…
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 reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We study the possibility that galactic rotation curves can be explained by a gravitational potential that contains a linear term as well as a Newtonian one. This hypothesis, suggested by conformal gravity, does allow good fits to the…
The classical model that describes the motion of an atom in a magnetic trap is solved in order to investigate the relationship between the failure of the usual adiabatic approximation assumption and the physical parameters of the trap. This…
We show within a statistical model of quantization reported in the previous work based on Hamilton-Jacobi theory with a random constraint that the statistics of fluctuations of the actual trajectories around the classical trajectories in…
We investigate oscillating solutions of the equation of motion for the Higgs potential. The solutions are described by Jacobian elliptic functions. Classifying the classical solutions, we evaluate a possible parameter-space for the initial…