Related papers: Nonlinearity-induced symmetry breaking in a system…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
We discuss a model of two nonlinear Kerr-like oscillators, mutually coupled and excited by parametric process. We show that the system's evolution, starting from Werner-like states, remains closed within a small set of two-mode n-photon…
In the present work, we explore the case of a general PT-symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave…
Optical systems that combine nonlinearity with coupling between various subsystems offer a flexible platform for observing a diverse range of nonlinear dynamics. Furthermore, engineering tolerances are such that the subsystems can be…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect i.e. interaction of optical waves with nonlinear medium with polarizability $\chi^{(3)}$ is the basic phenomenon needed to explain…
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability…
Nonlinear dynamics plays a significant role in interdisciplinary fields spanning biology, engineering, mathematics, and physics. Under small-amplitude approximations, certain nonlinear systems can be effectively described by the linear…
We study the symmetries of the static effective Hamiltonian of a driven superconducting nonlinear oscillator, the so-called squeeze-driven Kerr Hamiltonian, and discover a remarkable quasi-spin symmetry $su(2)$ at integer values of the…
Activation processes govern noise-induced switching between long-lived states. In an equilibrium double well, the thermally activated switching rate exhibits a prefactor with a nonmonotonic dependence on environmental coupling, a…
Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold, the field settles into a coherent oscillating state with a well-defined…
We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
An optical ring resonator with third-order, or Kerr, nonlinearity will exhibit symmetry breaking between the two counterpropagating circulating powers when pumped with sufficient power in both the clockwise and counterclockwise directions.…
We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry…
We investigate the quantum synchronization phenomena of two mechanical oscillators of different frequencies in two optomechanical systems under periodically modulating cavity detunings or driving amplitudes, which can interact mutually…
We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the…
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…
We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a…