Related papers: The period of a classical oscillator
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…
We introduce and discuss the method of Linear Delta Expansion for the calculation of effective potentials in superspace, by adopting the improved version of the super-Feynman rules. Calculations are carried out up to two-loops and an…
We consider the motion of a classical particle under the influence of a random potential on R^d, in particular the distribution of asymptotic velocities and the question of ergodicity of time evolution.
We apply the Linear Delta Expansion (LDE) to the Lindstedt-Poincare (``distorted time'') method to find improved approximate solutions to nonlinear problems. We find that our method works very well for a wide range of parameters in the case…
We analyze the motion of an overdamped classical particle in a multidimensional periodic potential, driven by a weak external noise. We demonstrate that in steady-state, the presence of temporal correlations in the noise and spatial…
The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated…
The limit cycle of the van der Pol oscillator, $\ddot{x}+ \epsilon (x^2-1) \dot{x} + x =0$, is studied in the plane $(x,\dot{x})$ by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form…
For a nonrelativistic classical particle undergoing arbitrary oscillations, the generalized effective potential Y is derived from nonlinear eigenfrequencies of the particle-field system. Specifically, the ponderomotive potential is extended…
It is proposed that the equations of motion in periodic relativity which yielded major predictions of general relativity are exact in nature and can be applied to pulsars and inspiraling compact binaries for analyzing orbital period…
For one dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, the semi-classical approximation to be exact. For velocity…
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…
We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force…
The optimized linear $\delta$-expansion is applied to the $\lambda \phi^4$ theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order $\delta^2$. A variational procedure…
An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.
In this note we discuss the usage of the Dirac $\delta$ function in models of phase oscillators with pulsatile inputs. Many authors use a product of the delta function and the phase response curve in the right hand side of an ODE to…
We calculate the first order maximal acceleration corrections to the classical electrodynamics of a particle in external electromagnetic fields. These include additional dissipation terms, the presence of a critical electric field, a…
This paper aims to shed some more light on one of the best known phenomena in the field of physics, the Doppler effect, in particular, on its classical version. Although, as mentioned, it is a phenomenon already described more than 150…
We propose and simulate a protocol to evolve a quantum particle forward in time such that its trajectory closely matches that of the particle's Newtonian counterpart. Using short bursts of Schr\"odinger time-evolution interleaved with…
The radiation spectrum of a classical charged particle (electron) moving in the de Sitter universe, has been calculated. The de Sitter metric is taken in the quasi-Euclidean Robertson-Walker form. It is shown that in the de Sitter spacetime…
Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian…