Related papers: Systematic perturbation calculation of integrals w…
We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as non-interacting, entangled systems, according to the Page and Wootters approach. We study how…
The difficulty that the probabilities infinitely increase with time as time is long enough in time-dependent perturbation theory for some quantum systems is resolved by means of simply transforming the perturbative series into natural…
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…
A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of…
Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles.…
Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of \lambda (Anharmonic Constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed…
An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context,…
The calculus of apsidal precession frequencies of the planets is developed by means of a perturbation thecnique. A model of concentric rings (ring model), suitable for improving calculations, is introduced. Conclusive remarks concerning a…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…
Given a planar differential system with a first integral, we show how to find a normalizer. For systems with a center, we give an integral formula for the derivative of its period function.
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
Discrete interaction models for the classical harmonic oscillator are used for introducing new mathematical generalizations in the usual continuous formalism. The inverted harmonic potential and generalized discrete hyperbolic and…