Related papers: Vector constants of motion for time-dependent Kepl…
We have simulated the ground states of quantum harmonic oscillators driven either by constant forces of different magnitudes or time-dependent driving forces. The expectation values of position for various combinations of mass, natural…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
We search for time-dependent solutions for the 5-dimensional system of a scalar field canonically coupled to gravity. Time-independent and time-dependent scalar field configurations with the most general homogeneous and isotropic 4D metric…
A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant $G$, a vector field coupling $\omega$ and the vector field mass $\mu$ to vary with space and time. The equations of motion for a test…
Aims. New or refined methods for determining instantaneous scalar and vector pattern speeds from a restricted domain are developed, for applications in N-body simulations or in galaxies. Methods. The general feature used throughout follows…
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type…
This paper deals with global asymptotic stability of prolongations of flows induced by specific vector fields and their prolongations. The method used is based on various estimates of the flows.
In the Madelung-Bohm approach to quantum mechanics, we consider a (time dependent) phase that depends quadratically on position and show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided…
In this paper, we investigate a two dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a…
We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of…
Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
In this paper we address the question of whether it is possible to integrate time-dependent high-dimensional PDEs with hierarchical tensor methods and explicit time stepping schemes. To this end, we develop sufficient conditions for…
A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the…
A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in the study of the systems: the homogeneous potentials of…
We compare the path integral for transition functions in unimodular gravity and in general relativity. In unimodular gravity the cosmological constant is a property of states that are specified at the boundaries whereas in general…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…