The slow passage problem through a resonance is considered. As a model problem, we consider a damped harmonically-forced oscillator whose forcing frequency is slowly ramped linearly in time. The set-up is similar to the familiar slow passage through a Hopf bifurcation problem, where for slow variations of the control parameter, oscillations are delayed until the parameter has exceeded the criti...

In this paper we review the basic results concerning Wigner transform and critically discuss problem of reversibility. Then completely solve harmonic/inverted forced quantum oscillator in such a framework; eventually, tunnel effect for inverted is discussed.

The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the os...

The interaction of a quantum deformed oscillator with the environment is studied deriving a master equation whose form strongly depends on the type of deformation. PACS number(s): 03.70.+k, 02.50.-r Quantum groups [1] introduced as a mathematical description of deformed Lie algebras have given the possibility to generalize the notion of creation and annihiliation operators of the usual oscillat...

Received (Day Month Year) Revised (Day Month Year) In this paper, we study the behaviour of a MEMS oscillator by applying methods of nonlin-ear dynamics. We model the system as a kicked damped oscillator and obtain the iterative maps that describe the MEMS system. The dynamics of the maps are studied numerically: we present a study of limit cycles and their rotation numbers and show how the con...

We determine local Hamiltonians, Poisson structures and conserved measures for the linear ows on < 2 . We study ows around critical points as deformations of the harmonic oscillator (HO) and the free particle. In particular the damped harmonic oscillator (DHO) is Hamiltonian with respect to non-standard Poisson structures for all non-zero values of the damping constant. Treating the DHO as a de...

We show that quantum Bateman’s system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy ...

By applying active control to an oscillator, its modal behaviour changes. This paper makes a comparison between a second order damped harmonic oscillator and a xylophone bar’s mode. Then it proposes a method for acting on an eigen resonance of a xylophone bar. The purpose is to get sound modifications, by bringing under quantitative and independent control its pitch and its duration. Thus it ex...