Virial theorems for vortex states in a confined Bose-Einstein condensate

We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed

Scattering of magnetic solitons in two dimensions

Solitons which have the form of a vortex-antivortex pair have recently been found in the Landau-Lifshitz equation which is the standard model for the ferromagnet. We simulate numerically head-on collisions of two vortex-antivortex pairs and observe a right angle scattering pattern. We offer a resolution of this highly nontrivial dynamical behavior by examining the Hamiltonian structure of the model, specifically the linear momentum of the two solitons. We further investigate the dynamics of vortices in a modified nonlinear sigma-model which arises in the description of antiferromagnets. We confirm numerically that a robust feature of the dynamics is the right angle scattering of two vortices which collide head-on. A generalization of our theory is given for this model which offers arguments towards an understanding of the observed dynamical behavior.Comment: 10 pages RevTeX, 9 figure

Magnon dispersion and thermodynamics in CsNiF_3

We present an accurate transfer matrix renormalization group calculation of the thermodynamics in a quantum spin-1 planar ferromagnetic chain. We also calculate the field dependence of the magnon gap and confirm the accuracy of the magnon dispersion derived earlier through an 1/n expansion. We are thus able to examine the validity of a number of previous calculations and further analyze a wide range of experiments on CsNiF_3 concerning the magnon dispersion, magnetization, susceptibility, and specific heat. Although it is not possible to account for all data with a single set of parameters, the overall qualitative agreement is good and the remaining discrepancies may reflect departure from ideal quasi-one-dimensional model behavior. Finally, we present some indirect evidence to the effect that the popular interpretation of the excess specific heat in terms of sine-Gordon solitons may not be appropriate.Comment: 9 pages 10 figure

Magnetic excitations in the spin-1 anisotropic antiferromagnet NiCl2−4SC(NH2)2NiCl_2-4SC(NH_2)_2

The spin-1 anisotropic antiferromagnet NiCl_2-4SC(NH2)_2 exhibits a field-induced quantum phase transition that is formally analogous to Bose-Einstein condensation. Here we present results of systematic high-field electron spin resonance (ESR) experimental and theoretical studies of this compound with a special emphasis on single-ion two-magnon bound states. In order to clarify some remaining discrepancies between theory and experiment, the frequency-field dependence of magnetic excitations in this material is reanalyzed. In particular, a more comprehensive interpretation of the experimental signature of single-ion two-magnon bound states is shown to be fully consistent with theoretical results. We also clarify the structure of the ESR spectrum in the so-called intermediate phase.Comment: 9 pages, 10 figure

Equilibrium Cross Section of River Channels With Cohesive Erodible Banks

Predicting the equilibrium cross section of natural rivers has been widely investigated in fluvial morphology. Several approaches have been developed to meet this aim, starting from regime equations to the empirical formulations of Parker et al. (2007) and Wilkerson and Parker (2011), who proposed quasi-universal relations for describing bankfull conditions in sand and gravel bed rivers. Nevertheless, a general physics-based framework is still missing, and it remains an open issue to better clarify the basic mechanisms whereby a river selects its width. In this contribution we focus our attention on lowland rivers with cohesive banks, whose resistance to erosion is crucial to control the river width. In particular, we formulate a theoretical model that evaluates the equilibrium width of river cross sections modeling the interaction between the core flow in the central part of the section and the boundary layer that forms in the vicinity of the cohesive banks. The model computes the cross-section equilibrium configuration by which the shear stresses on the banks equal a critical threshold value. These stresses are computed by partitioning the total shear stress into an effective grain roughness component and a form component (Kean and Smith, 2006a). The model is applied to a large data set, concerning both sand and gravel bed rivers, and it is used to determine the relations expressing the channel width and the bankfull flow depth to the bankfull discharge, which appear to provide a unitary description of bankfull hydraulic geometry

Solitary Waves of Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect

A branch of uniformly-propagating solitary waves of planar ferromagnets is identified. The energy dispersion and structures of the solitary waves are determined for an isotropic ferromagnet as functions of a conserved momentum. With increasing momentum, their structure undergoes a transition from a form ressembling a droplet of spin-waves to a Skyrmion/anti-Skyrmion pair. An instability to the formation of these solitary waves is shown to provide a mechanism for the electric field-induced breakdown of the spin-polarized quantum Hall effect.Comment: 5 pages, 3 eps-figures, revtex with epsf.tex and multicol.st

Nonlinear waves in a cylindrical Bose-Einstein condensate

We present a complete calculation of solitary waves propagating in a steady state with constant velocity v along a cigar-shaped Bose-Einstein trap approximated as infinitely-long cylindrical. For sufficiently weak couplings (densities) the main features of the calculated solitons could be captured by effective one-dimensional (1D) models. However, for stronger couplings of practical interest, the relevant solitary waves are found to be hybrids of quasi-1D solitons and 3D vortex rings. An interesting hierarchy of vortex rings occurs as the effective coupling constant is increased through a sequence of critical values. The energy-momentum dispersion of the above structures is shown to exhibit characteristics similar to a mode proposed sometime ago by Lieb within a strictly 1D model, as well as some rotonlike features.Comment: 10 pages, 12 figure