Related papers: A Forced Harmonic Oscillator, Interpreted as Diffr…
We prove that, under the condition of validity of the Fresnel approximation, diffraction and interference for a wave traveling in the z-direction may be described in terms of the spreading in time of the transverse (x,y)-wave packet. The…
We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…
We present a class of models in which the coupling of the photon to an ultralight scalar field that has a time-dependent vacuum expectation value causes the fine structure constant to oscillate in time. The scalar field is assumed to…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
In order to investigate the long-term dimensional stability of matter, we have operated an optical resonator fabricated from crystalline silicon at 1.5$\,$K continuously for over one year and repeatedly compared its resonance frequency…
Power laws in time and frequency appear in fields such as linear viscoelasticity and acoustics, viscous boundary layer problems, and dielectrics. This is consistent with fractional derivatives in the fundamental descriptions, since power…
Location of non-stationary forced oscillation (FO) sources can be a challenging task, especially in cases under resonance condition with natural system modes, where the magnitudes of the oscillations could be greater in places far from the…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
A critical review of frequency-shift phenomena a la Doppler effect is presented. The importance of Fermi's theory of 1932 is pointed out, and it is argued that there exists a gap in our understanding of this phenomena at a fundamental…
Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the…
It is explained how the time evolution of the operadic variables may be introduced. As an example, an operadic Lax representation of the harmonic oscillator is considered.
In this paper we review the basic results concerning the Wigner transform and then we completely solve the quantum forced harmonic/inverted oscillator in such a framework; eventually, the tunnel effect for the forced inverted oscillator is…
We present sufficient conditions for the existence of forced oscillations in non-autonomous mechanical systems. Previously, similar results were obtained for systems with friction. Presented results hold both for systems with and without…
Time-reflection is a uniform inversion of the temporal evolution of a signal, which arises when an abrupt change in the properties of the host material occurs uniformly in space. At such a time-interface, a portion of the input signal is…
Friction is a complex phenomenon that is of paramount importance in everyday life. We present an easy-to-build and inexpensive experiment illustrating Coulomb's law of kinetic friction. The so-called friction, or Timoshenko, oscillator…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
Novel optical elements containing semitransparent wavelike films embedded into the bulk of transparent material, which form a reflection image without transmitted light distortion, are studied. The dynamic theory of light diffraction by a…
Numerical and experimental evidence is presented to show that many phase synchronized systems of non-identical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the…
The dynamical backaction from a periodically driven optical or microwave cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Fundamentally, the driving…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…