Nonlinear localized modes in Glauber-Fock photonic lattices

We study a nonlinear Glauber-Fock lattice and the conditions for the excitation of localized structures. We investigate the particular linear properties of these lattices, including linear localized modes. We investigate numerically nonlinear modes centered in each site of the lattice. We found a strong disagreement of the general tendency between the stationary and the dynamical excitation thresholds. We define a new parameter that takes into account the stationary and dynamical properties of localized excitations.     

Nonstationary effects in the system of coupled quantum dots influenced by Coulomb correlations

We investigate the time evolution of filling numbers of localized electrons in the system of two coupled single-level quantum dots (QDs) connected with the continuous-spectrum states in the presence of Coulomb interaction. We consider correlation functions of all orders for electrons in the QDs by decoupling higher-order correlations between localized and band electrons in the reservoir. We analyze different initial charge configurations and consider Coulomb correlations between localized electrons both within the dots and between the different dots. We reveal the presence of a dynamical charge trapping effect in the first QD in the situation where both dots are occupied at the initial instant. We also find an analytic solution for the time-dependent filling numbers of the localized electrons for a particular configuration of the dots.     

Localized patterns in reaction-diffusion systems

We discuss a variety of experimental and theoretical studies of localized stationary spots, oscillons, and localized oscillatory clusters, moving and breathing spots, and localized waves in reaction-diffusion systems. We also suggest some promising directions for future research in this area.     

Localized mode hybridization by fine tuning of two-dimensional random media

We study numerically the interaction of spatially localized modes in strongly scattering two-dimensional (2D) media. We move eigenvalues in the complex plane by changing gradually the index of a single scatterer. When spatial and spectral overlap is sufficient, localized states couple, and avoided level crossing is observed. We show that local manipulation of the disordered structure can couple several localized states to form an extended chain of hybridized modes crossing the entire sample, thus changing the nature of certain modes from localized to extended in a nominally localized disordered system. We suggest such a chain in 2D random systems is the analog of one-dimensional necklace states, the occasional open channels predicted by Pendry [Physics 1, 20 (2008).] through which the light can sneak through an opaque medium.     

On the possibility of electric transport mediated by long living intrinsic localized solectron modes

We consider a polaron Hamiltonian in which not only the lattice and the electron-lattice interactions, but also the electron hopping term is affected by anharmonicity. We find that the one-electron ground states of this system are localized in a wide range of the parameter space. Furthermore, low energy excited states, generated either by additional momenta in the lattice sites or by appropriate initial electron conditions, lead to states constituted by a localized electron density and an associated lattice distortion, which move together through the system, at subsonic or supersonic velocities. Thus we investigate here the localized states above the ground state which correspond to moving electrons. We show that besides the stationary localized electron states (proper polaron states) there exist moving localized solectron states which can be easily excited. The evolution of these localized states suggests their potential as new carriers for fast electric charge transport.     

Curvature instability in passive diffractive resonators

We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.     

Surface waves at the interface between a metal and a photovoltaic-photorefractive crystal

We investigate surface waves at the interface between a metal and a photovoltaic-photorefractive (PP) crystal. These surface waves appear in several forms: delocalized surface waves, shock surface waves, and localized surface waves. Only localized surface waves have limited energy. We demonstrate that the transverse sizes of localized surface waves decrease with an increase in the propagation constant and the amplitudes of localized surface waves increase with the propagation constant. The stability of localized surface waves is investigated numerically and it is found that they are stable.     

Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber

We show the spontaneous and controlled formation of bistable and localized laser spots in the transverse section of a monolithic vertical cavity laser with a saturable absorber. Successive incoherent writing and erasure is obtained up to 80 MHz repetition rate with a 60 ps localized excitation. We also show the formation of clusters of laser localized states. All these observations are in good qualitative agreement with existing models.     

Fermions on colliding branes

We study the behaviour of five-dimensional fermions localized on branes, which we describe by domain walls, when two parallel branes collide in a five-dimensional Minkowski background spacetime. We find that most fermions are localized on both branes as a whole even after collision. However, how much fermions are localized on which brane depends sensitively on the incident velocity and the coupling constants unless the fermions exist on both branes.     

Families of Localized and Oscillatory Solutions to the Coupled-Nonlinear Two-Dimensional Dirac Equations

We numerically solve the coupled-nonlinear two-dimensional Dirac equations that describe a virtual spin-1/2 system with cubic nonlinearity.We find that this set of equations supports only oscillatory solutions in the non-relativistic limit and families of discrete localized solutions in the relativistic limit. Each family of the localized solutions is characterized by a constant central amplitude value. Each solution within a family is characterized by a number of nodes and a discrete energy eigenvalue, which is bounded by the rest mass of the particle. We study the effect of different parameters on the localized solutions.     

Evolution of III-V nitride alloy electronic structure: the localized to delocalized transition

Addition of nitrogen to III-V semiconductor alloys radically changes their electronic properties. We report large-scale electronic structure calculations of GaAsN and GaPN using an approach that allows arbitrary states to emerge, couple, and evolve with composition. We find a novel mechanism of alloy formation where localized cluster states within the gap are gradually overtaken by a downwards moving conduction band edge, composed of both localized and delocalized states. This localized to delocalized transition explains many of the hitherto puzzling experimentally observed anomalies in III-V nitride alloys.     

An ab-initio study of silicon adsorption on metallic surfaces (Au/Ag): Novel perspective to explore chemical bonding

We analyzed localized charge time evolution in the system of two interacting quantum dots (QD) (artificial molecule) coupled with the continuous spectrum states. We demonstrated that Coulomb interaction modifies relaxation rates and is responsible for non-monotonic time evolution of the localized charge. We suggested new mechanism of this non-monotonic charge time evolution connected with charge redistribution between different relaxation channels in each QD.     

The role of power law nonlinearity in the discrete nonlinear Schrödinger equation on the formation of stationary localized states in the Cayley tree

We study the formation of stationary localized states using the discrete nonlinear Schr?dinger equation in a Cayley tree with connectivity K. Two cases, namely, a dimeric power law nonlinear impurity and a fully nonlinear system are considered. We introduce a transformation which reduces the Cayley tree into an one dimensional chain with a bond defect. The hopping matrix element between the impurity sites is reduced by . The transformed system is also shown to yield tight binding Green's function of the Cayley tree. The dimeric ansatz is used to find the reduced Hamiltonian of the system. Stationary localized states are found from the fixed point equations of the Hamiltonian of the reduced dynamical system. We discuss the existence of different kinds of localized states. We have also analyzed the formation of localized states in one dimensional system with a bond defect and nonlinearity which does not correspond to a Cayley tree. Stability of the states is discussed and stability diagram is presented for few cases. In all cases the total phase diagram for localized states have been presented. Received: 18 September 1997 / Revised: 31 October and 17 november 1997 / Accepted: 19 November 1997     

Excitability mediated by localized structures in a dissipative nonlinear optical cavity

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.     

Dependence of resonance energy transfer on exciton dimensionality

We investigate the dependence of resonance energy transfer from Wannier-Mott excitons to an organic overlayer on exciton dimensionality. We exploit the excitonic potential disorder in a single quantum well to tune the balance between localized and free excitons by scaling the Boltzmann distribution of excitons through temperature. Theoretical calculations predict the experimentally observed temperature dependence of resonance energy transfer and allow us to quantify the contribution of localized and free excitons. We show that free excitons can undergo resonance energy transfer with an order of magnitude higher rate compared to localized excitons, emphasizing the potential of hybrid optoelectronic devices utilizing resonance energy transfer as a means to overcome charge transfer related limitations.     

Forcing and control of localized states in optical single feedback systems

Under feedback extended nonlinear optical systems spontaneously show a variety of periodic patterns and structures. Control gives new insight into these phenomena and it can open the way for potential application of nonlinear optical structures. We briefly review methods to control localized states in single feedback experiments. Application of a Fourier control method allows to modify interaction behavior of the localized states. As a further approach we study a forcing method, using externally created light fields as additional input to the system. Recent experiments show that the forcing method enables to favor addressing positions for localized structures. We demonstrate static addressing and favoring of addressing positions. We extend the forcing method to a dynamic forcing scheme, which allows to move and reposition localized states. Additionally forcing is used to balance experimental imperfections. PACS 05.45.Gg; 42.60.Jf; 42.65.Tg     

Quantum phase transition and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a double-well potential

We investigate the quantum phase transition (QPT) and dynamics induced by atom-pair tunnelling of Bose-Einstein condensates in a symmetric double well under the mean-field approximation. We find the system undergoes a new QPT towards phase-locking state when atom-pair tunnelling is strong enough, and the critical point of self-trapping QPT is shifted by atom-pair tunnelling. As for the dynamics, the system displays localized dynamical behaviour: phase-locking motion and self-trapping motion. We further study the correlation between this localized dynamics and QPT, and find that the area of the localized trajectories in the phase space can serve as an order parameter for both QPTs. The critical exponent of this order parameter is also discussed.     

Exact relaxation dynamics of a localized many-body state in the 1D Bose gas

Through an exact method, we numerically solve the time evolution of the density profile for an initially localized state in the one-dimensional bosons with repulsive short-range interactions. We show that a localized state with a density notch is constructed by superposing one-hole excitations. The initial density profile overlaps the plot of the squared amplitude of a dark soliton in the weak coupling regime. We observe the localized state collapsing into a flat profile in equilibrium for a large number of particles such as N=1000. The relaxation time increases as the coupling constant decreases, which suggests the existence of off-diagonal long-range order. We show a recurrence phenomenon for a small number of particles such as N=20.     

Nonlinear localized waves in a periodic medium

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.     

Non-stationary effects in the coupled quantum dots influenced by the electron-phonon interaction

We analyzed time evolution of the localized charge in the system of two interacting single level quantum dots coupled with the continuous spectrum states in the presence of electron-phonon interaction. We demonstrated that electron-phonon interaction leads to an increase in localized charge relaxation rate. We also found that several time scales with different relaxation rates appear in the system in the case of non-resonant tunneling between the dots. We revealed the formation of oscillations in the filling numbers time evolution caused by the emission and adsorption processes of phonons.