相关论文: Underdamped harmonic oscillator driven by a train …
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…
The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends…
We report a study on the ultrafast coherent population oscillations (UCPO) in two level atoms induced by the frequency modulated few-cycle optical pulse train. The phenomenon of UCPO is investigated by numerically solving the optical Bloch…
In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time-delayed attosecond pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is…
The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator…
It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary.…
Courses on undergraduate quantum mechanics usually focus on solutions of the Schr\"odinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced only academic examples are used, such as the…
We investigate the problem of two-level atoms driven by an ultrashort pulse train in the frequency domain. At low intensity regime, we obtain a perturbative analytical solution that allows us to discuss the role of the mode number of the…
A system of two coupled quantum harmonic oscillators with the Hamiltonian ${\hat H}=\frac{1}{2}\left(\frac{1}{m_1}{\hat p}^{2}_1 + \frac{1}{m_2}{\hat p}^{2}_2+A x^2_1+B x^2_2+ C x_1 x_2\right)$ can be found in many applications of quantum…
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of \lambda (Anharmonic Constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed…
In this paper, we determine the relativistic bound-state solutions for the Dirac oscillator (DO) in the curved spacetime of a cloud of strings in $(3+1)$-dimensions, where such solutions are given by the four-component normalized Dirac…
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…
We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to…