Related papers: The period of a classical oscillator
A specific class of explicitly time-dependent potentials is studied by means of path integrals. For this purpose a general formalism to treat explicitly time-dependent space-time transformations in path integrals is sketched. An explicit…
The interaction between freely propagating electrons and light waves is typically described using an approximation in which we assume that the electron velocity remains approximately the same during the interaction. In this article we…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
Plasma dipole oscillation (PDO) depicted as harmonic motion of a spatially localized block of electrons has, until now, been hypothetical. In practice, the plasma oscillation occurs always as a part of a plasma wave. Studies on radiation…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…
This paper formalize the existence's proof of first-integrals for any second order ODE, allowing to discriminate periodic orbits. Up to the author's knowledge, such a powerful result is not available in the literature providing a tool to…
The frequency of a classical periodic system can be obtained using action variables without solving the dynamical equations. We demonstrate the construction of two equivalent forms of the action variable for a one dimensional relativistic…
The 1-D dimension harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. In the…
This paper is devoted to a simple and short proof on the sharp upper bound of lifespan of classical solutions to wave equations with the critical power nonlinearities of spatial derivatives of the unknown function. Such a proof is so-called…
An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this…
We consider the motion of a charge in a large amplitude electrostatic wave with a triangular wave form relevant to an oscillating model of a pulsar magnetosphere. The (one-dimensional) orbit of a particle in such a wave is found exactly in…
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…
The time evolution of the correlation functions of an ensemble of anharmonic N-component oscillators with O(N) symmetry is described by a flow equation, exact up to corrections of order $1/N^2$. We find effective irreversibility.…
We compute the quadratic part of the thermal effective action for real scalar fields which are initially in thermal equilibrium and vary slowly in time using a generalised real-time formalism proposed by Le Bellac and Mabilat \cite{belmab}.…
We propose a simple linear scaling expression in reciprocal space for evaluating the ion--electron potential of crystalline solids. The expression replaces the long-range ion--electron potential with an equivalent localized charge…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
Classical molecular dynamics simulation is performed mostly using the established velocity Verlet integrator or other symplectic propagation schemes. In this work, an alternative formulation of numerical propagators for classical molecular…
This is an annotated translation of E126 'De novo genere oscillationum', in which Euler derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely, the motion of an…