Soliton pinning by long-range order in aperiodic systems

We investigate propagation of a kink soliton along inhomogeneous chains with two different constituents, arranged either periodically, aperiodically, or randomly. For the discrete sine-Gordon equation and the Fibonacci and Thue-Morse chains taken as examples, we have found that the phenomenology of aperiodic systems is very peculiar: On the one hand, they exhibit soliton pinning as in the random chain, although the depinning forces are clearly smaller. In addition, solitons are seen to propagate differently in the aperiodic chains than on periodic chains with large unit cells, given by approximations to the full aperiodic sequence. We show that most of these phenomena can be understood by means of simple collective coordinate arguments, with the exception of long range order effects. In the conclusion we comment on the interesting implications that our work could bring about in the field of solitons in molecular (e.g., DNA) chains.Comment: 4 pages, REVTeX 3.0 + epsf, 3 figures in accompanying PostScript file (Submitted to Phys Rev E Rapid Comm

Analytical approach to soliton ratchets in asymmetric potentials

We use soliton perturbation theory and collective coordinate ansatz to investigate the mechanism of soliton ratchets in a driven and damped asymmetric double sine-Gordon equation. We show that, at the second order of the perturbation scheme, the soliton internal vibrations can couple {\it effectively}, in presence of damping, to the motion of the center of mass, giving rise to transport. An analytical expression for the mean velocity of the soliton is derived. The results of our analysis confirm the internal mode mechanism of soliton ratchets proposed in [Phys. Rev. E {\bf 65} 025602(R) (2002)].Comment: 9 figures. Submitted to Phys. Rev.

Adiabatic Compression of Soliton Matter Waves

The evolution of atomic solitary waves in Bose-Einstein condensate (BEC) under adiabatic changes of the atomic scattering length is investigated. The variations of amplitude, width, and velocity of soliton are found for both spatial and time adiabatic variations. The possibility to use these variations to compress solitons up to very high local matter densities is shown both in absence and in presence of a parabolic confining potential.Comment: to appear in J.Phys.

Matter sound waves in two-component Bose-Einstein condensates

The creation and propagation of sound waves in two-component Bose-Einstein condensates (BEC) are investigated and a new method of wave generation in binary BEC mixtures is proposed. The method is based on a fast change of the inter-species interaction constant and is illustrated for two experimental settings: a drop-like condensate immersed into a second large repulsive condensate, and a binary mixture of two homogeneous repulsive BEC's. A mathematical model based on the linearized coupled Gross-Pitaevskii equations is developed and explicit formulae for the space and time dependence of sound waves are provided. Comparison of the analytical and numerical results shows excellent agreement, confirming the validity of the proposed approach.Comment: 16 pages, 9 figure

Shock waves in one-dimensional Heisenberg ferromagnets

We use SU(2) coherent state path integral formulation with the stationary phase approximation to investigate, both analytically and numerically, the existence of shock waves in the one- dimensional Heisenberg ferromagnets with anisotropic exchange interaction. As a result we show the existence of shock waves of two types,"bright" and "dark", which can be interpreted as moving magnetic domains.Comment: 10 pages, with 3 ps figure

Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin $1/2$ Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number $k$ fixing the polarization in the subsystem conservation of $S_{z}$ and with respect to the irreducible representations of the $\mathbf{S_{n}}$ group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the R\'{e}nyi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.Comment: Festschrift in honor of the 60th birthday of Professor Vladimir Korepin (11 pages, 5 figures

Wannier functions analysis of the nonlinear Schr\"{o}dinger equation with a periodic potential

In the present Letter we use the Wannier function basis to construct lattice approximations of the nonlinear Schr\"{o}dinger equation with a periodic potential. We show that the nonlinear Schr\"{o}dinger equation with a periodic potential is equivalent to a vector lattice with long-range interactions. For the case-example of the cosine potential we study the validity of the so-called tight-binding approximation i.e., the approximation when nearest neighbor interactions are dominant. The results are relevant to Bose-Einstein condensate theory as well as to other physical systems like, for example, electromagnetic wave propagation in nonlinear photonic crystals.Comment: 5 pages, 1 figure, submitted to Phys. Rev.

Multiregional Satellite Precipitation Products Evaluation over Complex Terrain

An extensive evaluation of nine global-scale high-resolution satellite-based rainfall (SBR) products is performed using a minimum of 6 years (within the period of 2000-13) of reference rainfall data derived from rain gauge networks in nine mountainous regions across the globe. The SBR products are compared to a recently released global reanalysis dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF). The study areas include the eastern Italian Alps, the Swiss Alps, the western Black Sea of Turkey, the French Cévennes, the Peruvian Andes, the Colombian Andes, the Himalayas over Nepal, the Blue Nile in East Africa, Taiwan, and the U.S. Rocky Mountains. Evaluation is performed at annual, monthly, and daily time scales and 0.25° spatial resolution. The SBR datasets are based on the following retrieval algorithms: Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis (TMPA), the NOAA/Climate Prediction Center morphing technique (CMORPH), Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN), and Global Satellite Mapping of Precipitation (GSMaP). SBR products are categorized into those that include gauge adjustment versus unadjusted. Results show that performance of SBR is highly dependent on the rainfall variability. Many SBR products usually underestimate wet season and overestimate dry season precipitation. The performance of gauge adjustment to the SBR products varies by region and depends greatly on the representativeness of the rain gauge network

Solitons in Tonks-Girardeau gas with dipolar interactions

The existence of bright solitons in the model of the Tonks-Girardeau (TG) gas with dipole-dipole (DD) interactions is reported. The governing equation is taken as the quintic nonlinear Schr\"{o}dinger equation (NLSE) with the nonlocal cubic term accounting for the DD attraction. In different regions of the parameter space (the dipole moment and atom number), matter-wave solitons feature flat-top or compacton-like shapes. For the flat-top states, the NLSE with the local cubic-quintic (CQ) nonlinearity is shown to be a good approximation. Specific dynamical effects are studied assuming that the strength of the DD interactions is ramped up or drops to zero. Generation of dark-soliton pairs in the gas shrinking under the action of the intensifying DD attraction is observed. Dark solitons exhibit the particle-like collision behavior. Peculiarities of dipole solitons in the TG gas are highlighted by comparison with the NLSE including the local CQ terms. Collisions between the solitons are studied too. In many cases, the collisions result in merger of the solitons into a breather, due to strong attraction between them.Comment: 15 pages, 8 figures, accepted by J. Phys. B: At. Mol. Opt. Phy