相关论文: Multidimensional localized states in externally dr…
Two-dimensional arrays of coupled waveguides or coupled microcavities allow to confine and manipulate light. Based on a paradigmatic envelope equation, we show that these devices, subject to a coherent optical injection, support coexistence…
We study theoretically transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria…
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 introduce a one-dimensional two-component system with the self-focusing cubic nonlinearity concentrated at a symmetric set of two spots. Effects of the spontaneous symmetry breaking (SSB) of localized modes were previously studied in the…
Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension substantial evidence for the existence of such…
The dynamics of a large array of coupled semiconductor lasers is studied for a nonlocal coupling scheme. Our focus is on chimera states, a self-organized spatio-temporal pattern of co-existing coherence and incoherence. In laser systems,…
We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…
We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pumping. In particular, we report on the excitability regime that cavity…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
Highly correlated biphoton states are powerful resources in quantum optics, both for fundamental tests of the theory and practical applications. In particular, high-dimensional spatial correlation has been used in several quantum…
An optical field inside a Fabry-Perot cavity would exhibit multistability either when an atomic medium, acting as a classical dielectric, is filled into the cavity or when the cavity becomes optomechanical where one reflecting end becomes…
We study the single-particle density of states of one-dimensional and two-dimensional quantum disordered systems with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two…
We discuss a two-dimensional system under the perturbation of a Moire potential, which takes the same geometry and lattice constant as the underlying lattices but mismatches up to relative rotation. Such a self-dual model belongs to the…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
This paper presents bilateral control laws for one-dimensional(1-D) linear 2x2 hyperbolic first-order systems (with spatially varying coefficients). Bilateral control means there are two actuators at each end of the domain. This situation…
In this article, we investigate the stabilizability of the two- and three-dimensional Navier-Stokes equations with memory effects around a non-constant steady state using a localized interior control. The system is first linearized around a…
In this work, the relation between input-to-state stability and integral input-to-state stability is studied for linear infinite-dimensional systems with an unbounded control operator. Although a special focus is laid on the case…
A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a…
We provide a thorough theoretical analysis of qubit state measurement in a setup where a driven, parametrically-coupled cavity system is directly coupled to the qubit, with one of the cavities having a weak Kerr nonlinearity. Such a system…