Related papers: Realizing limit cycles in dissipative bosonic syst…
We investigate the critical behavior of the open coherently-driven Bose-Hubbard dimer under nonlocal dissipation. A conserved quantity arises from the nonlocal nature of the dissipation, rendering the dimer multistable. In the weak-coupling…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
We investigate high-harmonic generation in closed systems, using the two-level atom as a simplified model. By means of a windowed Fourier transform of the time-dependent dipole acceleration, we extract the main contributions to this process…
Insights into complex phenomena in quantum matter can be gained from simulation experiments with ultracold atoms, especially in cases where theoretical characterization is challenging. However these experiments are mostly limited to…
A study of the Mode-locking lasing pulse formation in closed cavities is presented within a statistical mechanical framework where the onset of laser coincides with a thermodynamic phase transition driven by the optical power pumped into…
We propose a method for the generation of trains of alternating bright solitons in two-component Bose-Einstein condensates, using controlled emission of nonlinear matter-waves in the uncoupled regime with spatially-varying intra-species…
We classify symmetry-protected and symmetry-breaking dynamical solutions for nonlinear saturable bosonic systems that display a non-hermitian charge-conjugation symmetry, as realized in a series of recent groundbreaking experiments with…
Limit-cycle oscillators are the basic building blocks for synchronization; yet, the notion of a quantum limit cycle has remained unclear. Here, we study quantum limit cycles and synchronization in the presence of continuous heterodyne…
We present a detailed theoretical analysis of a peculiar generation of multiple bound states in the continuum (BICs) in two-dimensional periodic arrays of dielectric spheres. They emerge in high-symmetry lattices with the $C_{6v}$ and…
Time crystals constitute a novel phase of matter defined by the spontaneous breaking of timetranslation symmetry. Here we present a scheme to realize a continuous-time crystal of the vibrational phonon in the normal mode of two coupled…
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the…
The concept of optical bound states in the continuum (BICs) underpins the existence of strongly localized waves embedded into the radiation spectrum that can enhance the electromagnetic fields in subwavelength photonic structures. Early…
In recent years, the systems comprising of bosonic atoms confined to optical lattices at ultra-cold temperatures have demonstrated tremendous potential to unveil novel quantum mechanical effects appearing in lattice boson models with…
This study aims to provide evidence regarding the emergence of a class of dissipative time crystals when $\mathcal{PT}$ symmetry of the systems is restored in collective spin systems with Lindblad dynamics. First, we show that a standard…
In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
In this paper, we carry out a global qualitative analysis of a reduced planar quartic Topp system which models the dynamics of diabetes. In particular, studying global bifurcations, we prove that such a system can have at most two limit…
We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…