Related papers: A Forced Harmonic Oscillator, Interpreted as Diffr…
The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…
We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancila is dynamically…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to…
If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs:…
We derive analytical expressions to describe how light is frequency-shifted when interacting with ultrasound within scattering media, due to the modulation of the refractive index induced by the ultrasound pressure waves. The model is…
Time-dependent frequency harmonic oscillators (TDFHO's) are studied through the theory of Lie systems. We show that they are related to a certain kind of equations in the Lie group SL(2,R). Some integrability conditions appear as conditions…
We study the evolution of quantum fluctuations in systems known as time crystals, hypothetical systems for which the lowest energy state performs a periodic motion. We first discuss some general properties shared by time crystals, and…
The frequency shift of light in the gravitational field generated by a rotating body is investigated. We consider the scenario in which both the light source and the observer are in motion. The frequency shift is calculated up to the…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
The use of averaging has long been known to reduce noise in statistically independent systems that exhibit similar levels of stochastic fluctuation. This concept of averaging is general and applies to a wide variety of physical and man-made…
In a gravitational lensing system, the relative transverse velocities of the lens, source, and observer induce a frequency shift in the observed radiation. While this shift is typically negligible in most astrophysical contexts, strategies…
We investigate the question, "how does time flow?" and show that time may change by inversions as well. We discuss its implications to a simple class of linear systems. Instead of introducing any unphysical behaviour, inversions can lead to…
We consider single particle and polymer translocation where the frictional properties experienced from the environment are changing in time. This work is motivated by the interesting frequency responsive behaviour observed when a polymer is…
This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the…
Feynman propagator is calculated for the time dependent harmonic oscillator by converting the problem into a free particle motion
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…
We present an instructive way to introduce the subject of resonance using a typical spring-mass system without damping. In contrast to the standard approach found in most textbooks, here we propose a way to extend the lectures from common…
We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a…
Coherent time is a characteristic time in the extreme nonlinear optics regime and thus generally introduced as the dephasing time in the simulations of the solid-state high-harmonic generation. This characteristic time linked with the…