Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates

We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also studied numerically. Both cases of purely one-dimensional and ``cigar-shaped'' condensates are studied by means of different mean-field models, and the oscillation frequencies of the pertinent solitons are found and compared with the results obtained by the linear stability analysis.Numerical results are shown to be in very good agreement with the corresponding analytical predictions

Dark Breathers in Granular Crystals

We present a study of the existence, stability and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that bifurcate with the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors knowledge, has not been observed in classical Fermi- Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic way by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals

Invariant currents in lossy acoustic waveguides with complete local symmetry

We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry related spatial domains. Using experimental data we verify this mapping with remarkable accuracy. For the performed experiment we employ a construction technique based on local symmetries which allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal the fundamental role of symmetries in restricted spatial domains and clearly indicate that completely locally symmetric devices constitute a promising class of setups, regarding the manipulation of wave propagation.Comment: 11 pages, 5 figure

Avoiding Infrared Catastrophes in Trapped Bose-Einstein Condensates

This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in ``cigar-shaped'' (1D) attractive BECs and the transverse instability of dark solitons in ``pancake'' (2D) repulsive BECs. We suggest mechanisms, and give explicit estimates, on how to ``engineer'' the trapping conditions of the condensate to avoid such instabilities: the main result being that a tight enough trapping potential suppresses the instabilities present in the homogeneous limit. We compare the obtained estimates with numerical results and we highlight the relevant regimes of dynamical behavior

Defect Modes in One-Dimensional Granular Crystals

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We measure the near-linear frequency spectrum within the spatial vicinity of the defects, and identify the frequencies of the localized defect modes. We compare the experimentally determined frequencies with those obtained by numerical eigen-analysis and by analytical expressions based on few-site considerations. We also present a brief numerical and experimental example of the nonlinear generalization of a single-defect localized mode

Duality of bounded and scattering wave systems with local symmetries

We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domain-wise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard wall boundaries leads to extrema of the eigenenergies. The underlying wavefunction becomes then an eigenstate of the local symmetry transform in each of the domains of local symmetry. These extrema accumulate towards eigenenergies which do not depend on the position of the potentials inside the walls. They correspond to perfect transmission resonances of the associated scattering setup, obtained by removing the hard walls. We argue that this property characterizes the duality between scattering and bounded systems in the presence of local symmetries. Our findings are illustrated at hand of a numerical example with a potential consisting of two domains of local symmetry, each one comprised of Dirac ? barriers.Comment: 8 pages, 6 figure