Related papers: The transient route to resonance
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Unique set of coherent states for the anharmonic oscillator is obtained by requiring i. under the quantum mechanical time evolution a coherent state evolves into another, governed by trajectory in the classical phase space (of a related…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
If the damping of a simple harmonic oscillator from a thermally random force is sufficiently strong, then the oscillator may become unstable. For a photon oscillator (radiatively damped by electric dipole moments), the instability leads to…
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of…
Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…
This paper analyses the Hamiltonian model of drift waves which describes the chaotic transport of particles in the plasma confinement. With one drift wave the system is integrable and it presents stable orbits. When one wave is added the…
In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of…
Sustained oscillations (SOs) are commonly observed in systems dominated by converters. Under specific conditions, even though the origin of SOs can be identified through negative damping modes using conventional linear analysis, utilizing…
Non-autonomous perturbations of isochronous systems in the plane are considered. It is assumed that the intensity of perturbations decays with time, and the frequency is asymptotically constant with the limiting value satisfying a resonance…
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…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancila is dynamically…
We consider two technical developments of the formalism of continuous-time histories. First, we provide an explicit description of histories of the simple harmonic oscillator on the classical histories phase space, comparing and contrasting…
It is explained how the time evolution of the operadic variables may be introduced. As an example, an operadic Lax representation of the harmonic oscillator is considered.
The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space…
The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…