Selftrapping has been traditionally studied on the assumption that quasiparticles interact with harmonic phonons and that this interaction is linear in the displacement of the phonon. To complement recent semiclassical studies of anharmonicity and nonlinearity in this context, we present below a fully quantum mechanical analysis of a two-site system, where the oscillator is described by a tunab...

• The architecture of chaos oscillator should be similar to classical second order sine wave oscillator, e.g. LC or Wien-bridge based circuit. • The oscillator should not be higher than the third order system. • The circuit should be an autonomous oscillator. • The active unit should be linear and separated from the nonlinear element(s). • The nonlinear element should be single and simple, e.g....

A decomposition of a simplest mechanical system – a q-oscillator, is considered. A qoscillator (quasi-oscillator) is defined as a system consisting of a particle moving on a linear segment with a constant speed and reflecting from the segment’s end-points. A theorem, stating that a discrete-time version of q-oscillator can be decomposed into a countable set of discrete-time rotators (a rotator ...

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function, which can be tailored to one’s choice of stability requirement. This solves, once and for all, the problem of synchronous stability for any linear coupling of that oscillator. [...

We propose a general method for measuring an arbitrary observable of a multimode electromagnetic field using homodyne detection with a single local oscillator. In this method the local oscillator scans over all possible linear combinations of the modes. The case of two modes is analyzed in detail and the feasibility of the measurement is studied on the basis of Monte-Carlo simulations. We also ...

We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as suppressed by quantum fluctuations. Three different energy diffusions are observed in the kicked quantum harmonic oscillator, namely, localization, linear diffusion, and quadratic...

The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay angle of the generalized Harmonic oscillator. Explicitly time-dependent problems present special difficulties in classical and quantum mechanics. However, they...

 In this work, time domain analysis is used to solve Adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. Mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked LC and Ring oscillators considering their time-varying nature. Then, the analysis is verifie...