Related papers: A generalization of the Leeson effect

The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In additional to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also…

Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…

This work presents a new coupled array of frequency-adaptive Duffing oscillators. Based on learning rules, the natural frequency of each oscillator changes with the external excitation to achieve the frequency-adaptive capability in the…

We study an abstract model of an oscillator realized by an amplifier embedded in a positive feedback loop. The power and frequency stability of the output of such an oscillator are limited by quantum noise added by two elements in the loop:…

Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here we show that finite inertia of individual…

This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with a specific attention to phase resonance and to its relation with amplitude resonance. To this end, the different families of resonances, namely…

We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…

The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation…

The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…

Although "friction" is included in many models of oscillator damping, including viscous ones applied to the pendulum; they "miss the mark" with regard to a conceptual understanding of the mechanisms responsible for energy loss. The theory…

We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…

We study a resonator coupled to a generic detector and calculate the noise spectra of the two sub-systems. We describe the coupled system by a closed, linear, set of Langevin equations and derive a general form for the finite frequency…

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate…

Optomechanical oscillators (OMOs) combine the co-existing high quality factor mechanical and optical resonances in an integrated device to realize low phase noise RF oscillations. While several attempts have been demonstrated towards…

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS$_2$ and graphene membranes, used for both sensing and component-oriented applications.…

We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is…

We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…

We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case…

We extend our theory of Bloch oscillations of cold atoms inside an optical cavity [ Venkatesh et al. Phys. Rev. A 80 063834 (2009)] to include the effects of quantum noise arising from coupling to external modes. The noise acts as a form of…

We consider a population of globally coupled oscillators driven by common noise. By applying the Ott-Antonsen ansatz and by averaging over the fast oscillations, we obtain analytically tractable equations for the noisy evolution of the…