Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate

Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.Comment: 7 pages, 3 figure

Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation

Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied analytically in the framework of the forced extended Korteweg--de Vries (eKdV), or Gardner, equation. We consider both possible signs for the cubic nonlinear term in the Gardner equation corresponding to different fluid density stratification profiles. We identify the range of the input parameters: the oncoming flow speed (the Froude number) and the topographic amplitude, for which the obstacle supports a stationary localised hydraulic transition from the subcritical flow upstream to the supercritical flow downstream. Such a localised transcritical flow is resolved back into the equilibrium flow state away from the obstacle with the aid of unsteady coherent nonlinear wave structures propagating upstream and downstream. Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including solibores, rarefaction waves, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. The predictions of the developed analytic construction are confirmed by direct numerical simulations of the forced Gardner equation for a broad range of input parameters.Comment: 34 pages, 24 figure

Selective interlayer ferromagnetic coupling between the Cu spins in YBa2_2 Cu3_3 O7−x_{7-x} grown on top of La0.7_{0.7} Ca0.3_{0.3} MnO3_3

Studies to date on ferromagnet/d-wave superconductor heterostructures focus mainly on the effects at or near the interfaces while the response of bulk properties to heterostructuring is overlooked. Here we use resonant soft x-ray scattering spectroscopy to reveal a novel c-axis ferromagnetic coupling between the in-plane Cu spins in YBa$_2$ Cu$_3$ O$_{7-x}$ (YBCO) superconductor when it is grown on top of ferromagnetic La$_{0.7}$ Ca$_{0.3}$ MnO$_3$ (LCMO) manganite layer. This coupling, present in both normal and superconducting states of YBCO, is sensitive to the interfacial termination such that it is only observed in bilayers with MnO_2but not with La$_{0.7}$ Ca$_{0.3}$ interfacial termination. Such contrasting behaviors, we propose, are due to distinct energetic of CuO chain and CuO$_2$ plane at the La$_{0.7}$ Ca$_{0.3}$ and MnO$_2$ terminated interfaces respectively, therefore influencing the transfer of spin-polarized electrons from manganite to cuprate differently. Our findings suggest that the superconducting/ferromagnetic bilayers with proper interfacial engineering can be good candidates for searching the theorized Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in cuprates and studying the competing quantum orders in highly correlated electron systems.Comment: Please note the change of the title. Text might be slightly different from the published versio

Spontaneous Crystallization of Skyrmions and Fractional Vortices in the Fast-rotating and Rapidly-quenched Spin-1 Bose-Einstein Condensates

We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on the spin-1 Bose-Einstein condensates. By solving the stochastic projected Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a hexagonal lattice of skyrmions, and a square lattice of half-quantized vortices can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respetively, which can be imaged by using the polarization-dependent phase-contrast method

Delocalization and Diffusion Profile for Random Band Matrices

We consider Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by x,y \in (\bZ/L\bZ)^d, are independent, centred random variables with variances s_{xy} = \E |h_{xy}|^2. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\gg L^{4/5}$. We also show that the magnitude of the matrix entries \abs{G_{xy}}^2 of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute \E \abs{G_{xy}}^2. We show that, as $L\to\infty$ and $W\gg L^{4/5}$, the behaviour of \E |G_{xy}|^2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions

Speeding up Simplification of Polygonal Curves using Nested Approximations

We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm MR will have a complexity lower than the complexity of A. In particular, we show that if A has a O(N2/K) complexity (the complexity of a reduced search dynamic solution approach), where N and K are respectively the initial and the final number of segments, the complexity of MR is in O(N).We experimentally compare the outcomes of MR with those of the optimal "full search" dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either shows a lower complexity or provides polygonal approximations closer to the initial curves.Comment: 12 pages + figure

Hedgehog Spin-texture and Berry's Phase tuning in a Magnetic Topological Insulator

Understanding and control of spin degrees of freedom on the surfaces of topological materials are key to future applications as well as for realizing novel physics such as the axion electrodynamics associated with time-reversal (TR) symmetry breaking on the surface. We experimentally demonstrate magnetically induced spin reorientation phenomena simultaneous with a Dirac-metal to gapped-insulator transition on the surfaces of manganese-doped Bi2Se3 thin films. The resulting electronic groundstate exhibits unique hedgehog-like spin textures at low energies, which directly demonstrate the mechanics of TR symmetry breaking on the surface. We further show that an insulating gap induced by quantum tunnelling between surfaces exhibits spin texture modulation at low energies but respects TR invariance. These spin phenomena and the control of their Fermi surface geometrical phase first demonstrated in our experiments pave the way for the future realization of many predicted exotic magnetic phenomena of topological origin.Comment: 38 pages, 18 Figures, Includes new text, additional datasets and interpretation beyond arXiv:1206.2090, for the final published version see Nature Physics (2012