相关论文: Classical harmonic oscillator with Dirac-like para…

In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…

The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators…

We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures…

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…

Recent experimental progress in cavity optomechanics has allowed cooling of mesoscopic mechanical oscillators via dynamic backaction provided by the parametric coupling to either an optical or an electrical resonator. Here we analyze the…

We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…

We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…

A generalized Sellmeier model, also referred to as the Lorentz-Dirac model, has been used for the description of the dielectric function of a number of technologically important materials in the literature. This model represents the…

We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from the numerical point of view. We analytically prove the…

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…

We discuss the roles of the macroscopic limit and of different system-environment interactions in the quantum-classical transition for a chaotic system. We consider the kicked harmonic oscillator subject to reservoirs that correspond in the…

We analyse the properties of a strongly-damped quantum harmonic oscillator by means of an exact diagonalisation of the full Hamiltonian, including both the oscillator and the reservoir degrees of freedom to which it is coupled. Many of the…

Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is…

Using the modified Prelle- Singer approach, we point out that explicit time independent first integrals can be identified for the damped linear harmonic oscillator in different parameter regimes. Using these constants of motion, an…

The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…

We study the dynamics of a generalized version of the famous Kuramoto-Sakaguchi coupled oscillator model. In the classic version of this system, all oscillators are governed by the same ODE, which depends on the order parameter of the…

We investigate the one-dimensional Schr\"{o}dinger equation for a harmonic oscillator with a finite jump $a$ at the origin. The solution is constructed by employing the ordinary matching-of-wavefunctions technique. For the special choices…

Based on the tensor method, a q-analoque of the spin-orbit coupling is introduced in a q-deformed Schroedinger equation, previously derived for a central potential. Analytic expressions for the matrix elemnets of the representation j=l\pm…

The quantum dynamics of two-level systems under classical oscillator heat bath is mapped to the classical one of a charged particle under harmonic oscillator potential plus a magnetic field in a plane. The behavior of eigenstates and…

In this paper, we discuss a general procedure by which nonlinear power spectral densities (PSDs) of the harmonic oscillator can be calculated in both the quantum and classical regimes. We begin with an introduction of the damped and…