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.

Effect of thermal noise on the phase locking of a Josephson fluxon oscillator

The influence of thermal noise on fluxon motion in a long Josephson junction is investigated when the motion is phase locked to an external microwave signal. It is demonstrated that the thermal noise can be treated theoretically within the context of a two-dimensional map that models the dynamics of a single fluxon

π\pi-kinks in strongly ac driven sine-Gordon systems

We demonstrate that $\pi$-kinks exist in non-parametrically ac driven sine-Gordon systems if the ac drive is sufficiently fast. It is found that, at a critical value of the drive amplitude, there are two stable and two unstable equilibria in the sine-Gordon phase. The pairwise symmetry of these equilibria implies the existence of a one-parameter family of $\pi$-kink solutions in the reduced system. In the dissipative case of the ac driven sine-Gordon systems, corresponding to Josephson junctions, the velocity is selected by the balance between the perturbations. The results are derived from a perturbation analysis and verified by direct numerical simulations.Comment: 4 pages, 2 figures, revte

Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability

We show that the phenomenon of modulational instability in arrays of Bose-Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. These excitations represent thin disks in 1D, narrow tubes in 2D, and small hollows in 3D arrays, filled in with condensed atoms of much greater density compared to surrounding array sites. Aspects of the developed pattern depend on the initial distribution function of the condensate over the optical lattice, corresponding to particular points of the Brillouin zone. The long-time behavior of the spatial structures emerging due to modulational instability is characterized by the periodic recurrence to the initial low-density state in a finite optical lattice. We propose a simple way to retain the localized spatial structures with high atomic concentration, which may be of interest for applications. Theoretical model, based on the multiple scale expansion, describes the basic features of the phenomenon. Results of numerical simulations confirm the analytical predictions.Comment: 17 pages, 13 figure

Galactic Abundances: Report of Working Group 3

We summarize the various methods and their limitations and strengths to derive galactic abundances from in-situ and remote-sensing measurements, both from ground-based observations and from instruments in space. Because galactic abundances evolve in time and space it is important to obtain information with a variety of different methods covering different regions from the Very Local Insterstellar Medium (VLISM) to the distant galaxy, and different times throughout the evolution of the galaxy. We discuss the study of the present-day VLISM with neutral gas, pickup ions, and Anomalous Cosmic Rays, the study of the local interstellar medium (ISM) at distances <1.5 kpc utilizing absorption line measurements in H I clouds, and the study of galactic cosmic rays, sampling contemporary (~15 Myr) sources in the local ISM within a few kiloparsec of the solar system. Solar system abundances, derived from solar abundances and meteorite studies are discussed in several other chapters of this volume. They provide samples of matter from the ISM from the time of solar system format ion, about 4.5 Gyr ago. The evolution of galactic abundances on longer time scales is discussed in the context of nuclear synthesis in the various contributing stellar objects

Nonlinear excitations in arrays of Bose-Einstein condensates

The dynamics of localized excitations in array of Bose-Einstein condensates is investigated in the framework of the nonlinear lattice theory. The existence of temporarily stable ground states displaying an atomic population distributions localized on very few lattice sites (intrinsic localized modes), as well as, of atomic population distributions involving many lattice sites (envelope solitons), is studied both numerically and analytically. The origin and properties of these modes are shown to be inherently connected with the interplay between macroscopic quantum tunnelling and nonlinearity induced self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of these excitations is studied both for zero and non zero backgrounds. We find that in a definite range of parameters, homogeneous distributions can become modulationally unstable. We also show that bright solitons and excitations of shock wave type can exist in BEC arrays even in the case of positive scattering length. Finally, we argue that BEC array with negative scattering length in presence of linear potentials can display collapse.Comment: Submitted to Phys. Rev.