PT-symmetric lattices with spatially extended gain/loss are generically unstable

We illustrate, through a series of prototypical examples, that linear parity-time (PT) symmetric lattices with extended gain/loss profiles are generically unstable, for any non-zero value of the gain/loss coefficient. Our examples include a parabolic real potential with a linear imaginary part and the cases of no real and constant or linear imaginary potentials. On the other hand, this instability can be avoided and the spectrum can be real for localized or compact PT-symmetric potentials. The linear lattices are analyzed through discrete Fourier transform techniques complemented by numerical computations.Comment: 6 pages, 4 figure

Static and rotating domain-wall crosses in Bose-Einstein condensates

For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by intersection of two domain walls (DWs) separating immiscible species, with opposite signs of the wave functions in each pair of sectors filled by the same species. The cross pattern remains stable up to the zero value of the immiscibility parameter $|\Delta |$, while simpler rectilinear (quasi-1D) DWs exist only for values of $|\Delta |$ essentially exceeding those in BEC mixtures (two spin states of the same isotope) currently available to the experiment. Both symmetric and asymmetric cross configurations are investigated, with equal or different numbers $N_{1,2}$ of atoms in the two species. In rotating traps, ``propellers'' (stable revolving crosses) are found too. A full stability region for of the crosses and propellers in the system's parameter space is identified, unstable crosses evolving into arrays of vortex-antivortex pairs. Stable rotating rectilinear DWs are found too, at larger vlues of $|\Delta |$. All the patterns produced by the intersection of three or more DWs are unstable, rearranging themselves into ones with two DWs. Optical propellers are also predicted in a twisted nonlinear photonic-crystal fiber carrying two different wavelengths or circular polarizations, which can be used for applications to switching and routing.Comment: 9 pages, 10 figures, Phys. Rev. A (in press

Soliton Dynamics in Linearly Coupled Discrete Nonlinear Schr\"odinger Equations

We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical lattice. When the nonlinear coupling strengths are equal, we use a unitary transformation to remove the linear coupling terms, and show that the existing soliton solutions oscillate from one species to the other. When the nonlinear coupling strengths are different, the soliton dynamics is numerically investigated and the findings are compared to the results of an effective two-mode model. The case of two linearly coupled Ablowitz-Ladik equations is also investigated.Comment: to be published in Mathematics and Computers in Simulation, proceedings of the fifth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory (Athens, Georgia - April 2007

Multi-channel pulse dynamics in a stabilized Ginzburg-Landau system

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasi-elastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasi-elastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semi-quantitative agrement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasi-elastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed (WDM) transmission system.Comment: a text file in the revtex4 format, and 16 pdf files with figures. Physical Review E, in pres

Ag-coverage-dependent symmetry of the electronic states of the Pt(111)-Ag-Bi interface: The ARPES view of a structural transition

We studied by angle-resolved photoelectron spectroscopy the strain-related structural transition from a pseudomorphic monolayer (ML) to a striped incommensurate phase in an Ag thin film grown on Pt(111). We exploited the surfactant properties of Bi to grow ordered Pt(111)-xMLAg-Bi trilayers with 0 < x < 5 ML, and monitored the dispersion of the Bi-derived interface states to probe the structure of the underlying Ag film. We find that their symmetry changes from threefold to sixfold and back to threefold in the Ag coverage range studied. Together with previous scanning tunneling microscopy and photoelectron diffraction data, these results provide a consistent microscopic description of the coverage-dependent structural transition.Comment: 10 pages, 9 figure