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

Single vortex states in a confined Bose-Einstein condensate

It has been demonstrated experimentally that non-axially symmetric vortices precess around the centre of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S-vortex and the U-vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S-vortex has higher energy than the U-vortex in a rotating elongated condensate. We show that the S-vortex is related to the solitonic vortex which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S-vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states

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

Robust seismic velocity change estimation using ambient noise recordings

We consider the problem of seismic velocity change estimation using ambient noise recordings. Motivated by [23] we study how the velocity change estimation is affected by seasonal fluctuations in the noise sources. More precisely, we consider a numerical model and introduce spatio-temporal seasonal fluctuations in the noise sources. We show that indeed, as pointed out in [23], the stretching method is affected by these fluctuations and produces misleading apparent velocity variations which reduce dramatically the signal to noise ratio of the method. We also show that these apparent velocity variations can be eliminated by an adequate normalization of the cross-correlation functions. Theoretically we expect our approach to work as long as the seasonal fluctuations in the noise sources are uniform, an assumption which holds for closely located seismic stations. We illustrate with numerical simulations and real measurements that the proposed normalization significantly improves the accuracy of the velocity change estimation

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

Vortex Pull by an External Current

In the context of a dynamical Ginzburg-Landau model it is shown numerically that under the influence of a homogeneous external current J the vortex drifts against the current with velocity $V= -J$ in agreement to earlier analytical predictions. In the presence of dissipation the vortex undergoes skew deflection at an angle $90^{\circ} < \delta < 180^{\circ}$ with respect to the external current. It is shown analytically and verified numerically that the angle $\delta$ and the speed of the vortex are linked through a simple mathematical relation.Comment: 19 pages, LATEX, 6 Postscript figures included in separate compressed fil

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