Related papers: Nonlinear dynamics of weakly dissipative optomecha…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation…
The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is argued that chaos in this system has a very particular spatial…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…
In traditional research, chaos is frequently accompanied by non-linearity, which typically stems from non-linear interactions or external driving forces. However, in this paper, we present the chaotic behavior that is completely attributed…
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with…
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories…
We investigate semiclassical dynamics of a coupled atom-photon interacting system described by a dimer of anisotropic Dicke model in the presence of photon loss, exhibiting a rich variety of non-linear dynamics. Based on symmetries and…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…
An $S$--matrix approach is developed for the chaotic dynamics of a nonlinear oscillator with dissipation. The quantum--classical crossover is studied in the framework of the semiclassical expansion for the $S$--matrix. Analytical…
In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
We present non-linear dynamical features of two-photon double-cavity optical bistability exhibited by a three level ladder system in the mean field limit. The system exhibits a hump like feature in the lower branch of the bistable response,…
Nonlinear interactions in optomechanical systems play a crucial role in many emerging number of interesting studies and phenomena such as existence of optomechanical chaos introduced by F. Monifi et al. [Nature Photonics 10, 399405 (2016)]…
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress…
We study the nonlinear driven dissipative quantum dynamics of an array of optomechanical systems. At each site of such an array, a localized mechanical mode interacts with a laser-driven cavity mode via radiation pressure, and both photons…
Driven quantum nonlinear oscillators, while essential for quantum technologies, are generally prone to complex chaotic dynamics that fall beyond the reach of perturbative analysis. By focusing on subharmonic bifurcations of a harmonically…
Optical non-linearities, such as thermo-optic effects and free-carrier-dispersion, are often considered as undesired effects in silicon-based resonators and, more specifically, optomechanical (OM) cavities, affecting the relative detuning…
Hyperchaos is a qualitatively stronger form of chaos, in which several degrees of freedom contribute simultaneously to exponential divergence of small changes. A hyperchaotic dynamical system is therefore even more unpredictable than a…