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...

In addition to the passive observation of a non­ linear oscillator and the description of the measured data with Lyapounow exponents [1, 2], fractal dimensions [3-5], entropies [6], etc. it is possible to charcterize a non-linear oscillator by an active method, namely by determining its response to specific perturbations. The resonances of harmonic systems which are brought about by a sinusoida...

We model theoretically the response of the widely studied circadian oscillator of Neurospora crassa to inactivation of the frq gene. The resulting organism has been termed "arrhythmic" under constant conditions. Under entrainment to periodic temperature cycles Roenneberg, Merrow and coworkers have shown that the phase angle at which spore formation occurs depends on the entrainment period, curi...

The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by Liapunov’s direct method. The results are demonstrated by numerical calculations on the example of the damped harmonic oscillator.

6 Von Neumann Entropy 16 6.1 A Warmup Exercise: Damped Harmonic Oscillator . . . . . . 16 6.2 Double Well Coupled to a Dissipative Heat Bath . . . . . . . 17 6.3 Disordered Systems . . . . . . . . . . . . . . . . . . . . . . . . 19 6.3.1 Anderson Localization . . . . . . . . . . . . . . . . . . 20 6.3.2 Integer Quantum Hall Plateau Transitions . . . . . . . 21 6.3.3 Infinite Randomness Fixed Po...

Quantum dynamics of a general dissipative system investigated by its coupling to a Klein-Gordon type field as the environment by introducing a minimal coupling method. As an example, the quantum dynamics of a damped three dimensional harmonic oscillator investigated and some transition probabilities indicating the way energy flows between the subsystems obtained. The quantum dynamics of a dissi...

We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose solutions exactly coincide with solutions of the corresponding differential equation evaluated at a discrete sequence of points (a lattice). Such exact discret...

We discuss the fate of initial states of the cat type for the damped harmonic oscillator, mostly employing a linear version of the stochastic Schrödinger equation. We also comment on how such cat states might be prepared and on the relation of single realizations of the noise to single runs of experiments. Typeset using REVTEX 1

The nonequilibrium dynamics of a small quantum system coupled to a dissipative environment is studied. We show that (i) the oscillatory dynamics close to a coherent-to-incoherent transition is significantly different from the one of the classical damped harmonic oscillator and that (ii) non-Markovian memory plays a prominent role in the time evolution after a quantum quench.

The main aim of the paper is to present the analytical solution of the Belavkin quantum filtering equation for damped harmonic oscillator being initially in the squeezed coherent state for diffusion observation with complex white noise. The comparison of the a priori and a posteriori mean value of the optical quadrature operators and the photon number operator is given.