Related papers: Vortex ring beams in nonlinear $\mathcal{PT}$-symm…
We study two-component spatial optical solitons carrying an angular momentum and propagating in a self-focusing saturable nonlinear medium. When one of the components is small, such vector solitons can be viewed as a self-trapped vortex…
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…
The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where three states (domains) meet. We can…
Non-Hermitian systems with parity-time symmetry have been found to exhibit real spectra of eigenvalues, indicating a balance between the loss and gain. However, such a balance is not only dependent on the magnitude of loss and gain, but…
We study vortex states in a 3d random-field XY model of up to one billion lattice spins. Starting with random spin orientations, the sample freezes into the vortex-glass state with a stretched-exponential decay of spin correlations, having…
We address the stability of light bullets supported by Bessel optical lattices with out-of-phase modulation of the linear and nonlinear refractive indices. We show that spatial modulation of the nonlinearity significantly modifies the…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
The stability of periodic arrays of Mallier-Maslowe or Kelvin-Stuart vortices is discussed. We derive with the energy-Casimir stability method the nonlinear stability of this solution in the inviscid case as a function of the solution…
We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response…
We address the formation of topological states in twisted circular waveguide arrays and find that twisting leads to important differences of the fundamental properties of new vortex solitons with opposite topological charges that arise in…
We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase…
The effects of gain and loss on the band structures of a bulk topological dielectric photonic crystal (PC) with $C_{6v}$ symmetry and the PC-air-PC interface are studied based on first-principle calculation. To illustrate the importance of…
We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index…
Open quantum-system dynamics can follow exponential decay, non-exponential relaxation, or oscillatory dynamics, depending on the system-environment coupling. We study a lattice with a boundary defect that transitions between these regimes,…
The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…
The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a…
Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one…
We examine localized surface modes in the core of a photonic crystal fiber composed of a finite nonlinear (Kerr) hexagonal waveguide array with a central defect. Using a discrete approach, we find the fundamental surface mode and its…
Linear combinations of Bessel beams can be used to effectively trap light within cylindrical domains. Such hard traps can be used to produce states that exhibit stationary arrays of optical vortices from the perspective of a steadily…
A ring laser is defined by its perimeter, which directly enters the conversion factor between measured Sagnac frequency and the actual rotation rate. Large ring lasers employed in geodesy and fundamental physics require stability of the…