We studied the splitting instability of a quadruply charged vortex both experimentally and theoretically. The density defect, which is a signature of the vortex core, is experimentally observed to deform into a linear shape. The deformed defect is theoretically confirmed to be an array of four linearly aligned singly charged vortices. The array of vortices rotates and precesses simultaneously with different angular velocities. The initial state of the system is not rotationally symmetric, which enables spontaneous splitting without external perturbations.

We study stationary clusters of vortices and antivortices in dilute pancake-shaped Bose-Einstein condensates confined in nonrotating harmonic traps. Previous theoretical results on the stability properties of these topologically nontrivial excited states are seemingly contradicting. We clarify this situation by a systematic stability analysis. The energetic and dynamic stability of the clusters is determined from the corresponding elementary excitation spectra obtained by solving the Bogoliubov equations. Furthermore, we study the temporal evolution of the dynamically unstable clusters. The stability of the clusters and the characteristics of their destabilizing modes only depend on the effective strength of the interactions between particles and the trap anisotropy. For certain values of these parameters, there exist several dynamical instabilities, but we show that there are also regions in which some of the clusters are dynamically stable. Moreover, we observe that the dynamical instability of the clusters does not always imply their structural instability, and that for some dynamically unstable states annihilation of the vortices is followed by their regeneration, and revival of the cluster.

Recently, the splitting of a topologically created doubly quantized vortex into two singly quantized vortices was experimentally investigated in dilute atomic cigar-shaped Bose-Einstein condensates [Y. Shin, Phys. Rev. Lett. 93, 160406 (2004)10.1103/PhysRevLett.93.160406]. In particular, the dependency of the splitting time on the peak particle density was studied. We present results of theoretical simulations which closely mimic the experimental setup. We show that the combination of gravitational sag and time dependency of the trapping potential alone suffices to split the doubly quantized vortex in time scales which are in good agreement with the experiments.

Business ecosystems consist of a heterogeneous and continuously evolving set of entities that are interconnected through a complex, global network of relationships. However, there is no well-established methodology to study the dynamics of this network. Traditional approaches have primarily utilized a single source of data of relatively established firms; however, these approaches ignore the vast number of relevant activities that often occur at the individual and entrepreneurial levels. We argue that a data-driven visualization approach, using both institutionally and socially curated datasets, can provide important complementary, triangulated explanatory insights into the dynamics of interorganizational networks in general and business ecosystems in particular. We develop novel visualization layouts to help decision makers systemically identify and compare ecosystems. Using traditionally disconnected data sources on deals and alliance relationships (DARs), executive and funding relationships (EFRs), and public opinion and discourse (POD), we empirically illustrate our data-driven method of data triangulation and visualization techniques through three cases in the mobile industry Google’s acquisition of Motorola Mobility, the coopetitive relation between Apple and Samsung, and the strategic partnership between Nokia and Microsoft. The article concludes with implications and future research opportunities.

We numerically investigate vortex lattices in rotating two-component Bose-Einstein condensates in which the two components have unequal atomic masses and interact attractively with each other. For sufficiently strong attraction, the system is found to exhibit exotic ground-state structures in a harmonic trap, such as lattices having a square geometry or consisting of two-quantum vortices. The obtained states satisfy the Feynman relation, and they can be realized with current experimental techniques.Comment: 7 pages, 4 color figures; the content of v2 is identical to the published articl

We numerically investigate low-energy stationary states of pseudospin-1 Bose-Einstein condensates in the presence of Rashba-Dresselhaus-type spin-orbit coupling. We show that for experimentally feasible parameters and strong spin-orbit coupling, the ground state is a square vortex lattice irrespective of the nature of the spin-dependent interactions. For weak spin-orbit coupling, the lowest-energy state may host a single vortex. Furthermore, we analytically derive constraints that explain why certain stationary states do not emerge as ground states. Importantly, we show that the distinct stationary states can be observed experimentally by standard time-of-flight spinindependent absorption imaging.

Recently, Freilich et al. [Science 329, 1182 (2010)] experimentally discovered stationary states of vortex dipoles, pairs of vortices of opposite circulation, in dilute Bose-Einstein condensates. To explain their observations, we perform simulations based on the Gross-Pitaevskii equation and obtain excellent quantitative agreement on the size of the stationary dipole. We also investigate how their imaging method, in which atoms are repeatedly extracted from a single condensate, affects the vortex dynamics. We find that it mainly induces isotropic size oscillations of the condensate without otherwise disturbing the vortex trajectories. Thus, the imaging technique appears to be a promising tool for studying real-time superfluid dynamics.Comment: 4 pages, 3 figure

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