相关论文: Multidimensional localized states in externally dr…
Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous occurrence of a steady front between two spatially homogeneous equilibria and a supercritical Turing…
We introduce a one-dimensional model of a cavity with the Kerr nonlinearity and saturated gain, designed so as to keep solitons in the state of shuttle motion. The solitons are always unstable in the cavity bounded by the usual potential…
We investigate a bi-directionally coupled system consisting of a Kerr-nonlinear microresonator and a continuous-wave single-mode semiconductor laser. Inside the resonator, a forward-propagating and a backscattered field interact…
We analyze the formation of one-dimensional localized patterns in a nonlinear dissipative medium including a set of two narrow "hot spots" (HSs), which carry the linear gain, local potential, cubic self-interaction, and cubic loss, while…
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…
High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
We show that an optical system involving competing higher-order Kerr nonlinearities can support the existence of ultrasolitons, namely extremely localized modes that only appear above a certain threshold for the central intensity. Such new…
The interaction of a single-mode field with both a weak Kerr medium and a parametric nonlinearity in an intrinsically nonlinear optomechanical system is studied. The nonlinearities due to the optomechanical coupling and Kerr-down conversion…
The interplay of disorder and dimensionality governs the emergence and stability of electronic phases in quantum materials and quantum phase transitions among them. While three-dimensional (3D) dirty Fermi liquids and Weyl semimetals…
We theoretically analyze three-mode opto-acoustic parametric interactions in a coupled Fabry-Perot cavity, where one acoustic mode interacts with two optical modes. We show explicitly that extra degrees of freedom in a coupled cavity allow…
We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including…
We study nematic equilibria in an unbounded domain, with a two-dimensional regular polygonal hole with $K$ edges, in a reduced Landau-de Gennes framework. This complements our previous work on the "interior problem" for nematic equilibria…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
We study, analytically and numerically, the stationary states in the system of two linearly coupled nonlinear Schr{\"o}dinger equations in two spatial dimensions, with the nonlinear interaction coefficients of opposite signs. This system is…
We address the existence and stability of localized modes in the two-dimensional (2D) linear Schroedinger lattice with two symmetric nonlinear sites embedded into it, and a generalization for moderately localized nonlinearity featuring two…
A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong static imperfection in the unperturbed energy levels. The system…
As recently realized experimentally [L\'eonard et al., Nature 543, 87 (2017)], one can engineer models with continuous symmetries by coupling two cavity modes to trapped atoms, via a Raman pumping geometry. Considering specifically cases…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…