Related papers: Harmonic analysis of oscillators through standard …
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is…
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or…
We show that the algebraic method solving the ordinary harmonic oscillator can be adapted to the non-commutative case.
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…
Hybrid oscillator architectures that combine feedback oscillators with self-sustained negative resistance oscillators have emerged as a promising platform for artificial neuron design. In this work, we introduce a modeling and analysis…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
In this work, Lienard equations are considered. The limit cycles of these systems are studied by applying the homotopy analysis method. The amplitude and frequency obtained with this methodology are in good agreement with those calculated…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GW) in the long wave-length and low-velocity limit. Following the prescription in \cite{ncgw1} we…
Conventionally while we talk about geometry associated with a simple harmonic oscillator, we draw a circle with a radius equal to the amplitude of Oscillator and imagine a particle moving along the perimeter with a frequency same as that of…
Quantum harmonic oscillators are central to many modern quantum technologies. We introduce a method to determine the frequency noise spectrum of oscillator modes through coupling them to a qubit with continuously driven…
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…
In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting…
Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
We define Sturmian basis functions for the harmonic oscillator and investigate whether recent insights into Sturmians for Coulomb-like potentials can be extended to this important potential. We also treat many body problems such as coupling…
We take a qualitative comparative look at quantum and classical quartic anharmonic oscillators. It has been shown that the behavior of the quantum anharmonic oscillator mimics that of the classical anharmonic oscillators with the…
We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is crucial for application in analytic number…