Related papers: Driven generalized quantum Rayleigh-van der Pol os…
In this study we demonstrate a self-oscillating acoustic meta-atom functioning as an amplifying transistor, where a steady external flow serves as a control signal to switch between reflective (off-state) and transmissive (on-state)…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…
Different models of self-excited oscillators which are four-dimensional extensions of the van der Pol system are reported. Their symmetries are analyzed. Three of them were introduced to model the release of vortices behind circular…
We study the quantum phase synchronization of a driven two-level system (TLS) coupled to a structured environment and demonstrate that quantum synchronization can be enhanced by the classical driving field. We use the Husimi $Q$-function to…
The ubiquitous phenomenon of synchronization is inherently characteristic of dynamical dissipative non-linear systems. In particular, synchronization has been theoretically and experimentally demonstrated for exciton-polariton condensates…
Phase reduction is an effective theoretical and numerical tool for studying synchronization of coupled deterministic oscillators. Stochastic oscillators require new definitions of asymptotic phase. The $Q$-function, i.e. the slowest…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
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…
Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix…
We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…
We investigate collective nonlinear dynamics in a blue-detuned optomechanical cavity that is mechanically coupled to an undriven mechanical resonator. By controlling the strength of the driving field, we engineer a mechanical gain that…
We study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the…
We consider a Hamiltonian system of coupled Van der Pol-Duffing(VdPD) oscillators with balanced loss and gain. The system is analyzed perturbatively by using Renormalization Group(RG) techniques as well as Multiple Scale Analysis(MSA). Both…
The search for exotic temporal orders in quantum matter, such as discrete quasi-time crystals (DQTCs), has become an important theme in nonequilibrium physics. However, realizing these phases has so far required complex protocols, such as…
The de Broglie-Bohm quantum trajectories are found in analytically closed forms for the eigenstates and the coherent state of the Lewis-Riesenfeld (LR) invariant of a time-dependent harmonic oscillator. It is also shown that an eigenstate…
In this paper, we study the existence of bifurcation of a van der Pol-Duffing oscillator with quintic terms and its quasi-periodic solutions by means of qualitative and bifurcation theories. Firstly, we analyze the autonomous system and…
In this second in a series of four articles we create a mathematical formalism sufficient to represent nontrivial hamiltonian quantum dynamics, including resonances. Some parts of this construction are also mathematically necessary. The…