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Optical force can enable precise manipulations of small particles for various applications. It is well known that an isotropic lossless dielectric sphere is only subject to forward optical force under the illumination of an electromagnetic…
We study theoretically optomechanical damping and amplification spectra for vibrations interacting with excitonic polaritons in a zero-dimensional microcavity. We demonstrate, that the spectra strongly depend on the ratio of the…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
Following the Caldeira-Leggett approach to describe dissipative quantum systems the structure function for a harmonic oscillator with Ohmic dissipation is evaluated by an analytic continuation from euclidean to real time. The analytic…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
The vibrational properties of a high-quality realistic model of amorphous silicon are examined. The longitudinal and transverse dynamical structure factors are calculated, and fitted to a damped harmonic oscillator (DHO) function. The width…
In this paper, we consider estimates for the two-dimensional oscillatory integrals. The phase function of the oscillatory integrals is the linear perturbation of a function having $D$ type singularities. We consider estimates for the…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
We present the theory of dielectric spectra allowing for homogeneous and inhomogeneous broadening mechanisms contributions. The dielectric absorption line shape for oscillators with memory and Debye type relaxors with distribution of,…
We derive the frequency shifts and the broadening of $\Gamma$ point longitudinal optical (LO) and transverse optical (TO) phonon modes, due to electron-phonon interaction, in graphene under uniaxial strain as a function of the electron…
Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external…
We consider a model for two lasers that are mutually coupled optoelectronically by modulating the pump of one laser with the intensity deviations of the other. Signal propagation time in the optoelectronic loop causes a significant delay…
The oscillator, inherently, turns the phase noise of its internal components into frequency noise, which results into a multiplication by 1/f^2 in the phase-noise power spectral density. This phenomenon is known as the Leeson effect. This…
Massive quantum oscillators are finding increasing applications in proposals for high-precision quantum sensors and interferometric detection of weak forces. Although optimal estimation of certain properties of massive quantum oscillators…
The Fresnel-Snell law, which is one of the fundamental laws in optics and gives insights on the behaviour of light at interfaces, is violated if there exists dissipation in the transmitting media. In order to overcome this problem, we…
We extend Kramers-Kronig relations beyond the optical approximation to dielectric functions that depend not only on frequency but on the wave number as well. This implies extending the notion of causality commonly used in the theory of…
The general theory of time-dependent frequency and time-dependent mass ('effective mass') is described.The general theory for time-dependent harmonic- oscillator is applied in the present research for studying certain quantum effects in the…
For incidence in the critical region, the propagation of gaussian lasers through triangular dielectric blocks is characterized by the joint action of angular deviations and lateral displacements. This mixed effect, known as composite…
In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on $\mathbb{R}^d$ isomorphic to $\mathbb{Z}^d_2$. We prove that imaginary powers of this operator are…
The existence of large nonlinear optical coefficients is one of the preconditions for using nonlinear optical materials in nonlinear optical devices. For a crystal, such large coefficients can be achieved by matching photon energies with…