Related papers: Enhanced stability, bistability, and exceptional p…
Topological photonics has emerged recently as a novel approach for realizing robust optical circuitry, and the study of nonlinear effects in topological photonics is expected to open the door for tunability of photonic structures with…
A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a…
Understanding and characterizing phase transitions in driven-dissipative systems constitutes a new frontier for many-body physics. A generic feature of dissipative phase transitions is a vanishing gap in the Liouvillian spectrum, which…
We introduce a class of one-dimensional complex optical potentials that feature a nonlinearity-induced stability restoration, i.e., the existence of stable nonlinear modes propagating in a waveguide whose linear eigenmodes are unstable. The…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and…
Three-body interactions have been found in physics, biology, and sociology. To investigate their effect on dynamical systems, as a first step, we study numerically and theoretically a system of phase oscillators with three-body interaction.…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing…
The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed…
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we…
We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective…
Exceptional points are a ubiquitous concept widely present in driven-dissipative coupled systems described by a non-Hermitian Hamiltonian. It is characterized by the degeneracy of the Hamiltonian's eigenvalues and coalescence of…
We introduce a simple model system to study synchronization theoretically in quantum oscillators that are not just in limit-cycle states, but rather display a more complex bistable dynamics. Our oscillator model is purely dissipative, with…
Rapidly growing demands for fast information processing have launched a race for creating compact and highly efficient optical devices that can reliably transmit signals without losses. Recently discovered topological phases of light…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Theories in physics can provide a kind of map of the physical system under investigation, showing all of the possible types of behavior which may occur. Certain points on the map are of greater significance than others, because they…
We theoretically investigate the optical bistability phenomenon in an ensemble of $N$ non-interacting three-level atoms trapped inside an optical cavity. The atoms are in a $\Lambda$-level configuration, where one atomic transition is…
We explore theoretically the bistable behavior of intracavity photon number in a two-mode cavity optomechanical system, where two cavity modes are coupled to a common mechanical resonator. When the two cavity modes are driven by two pump…
The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…