Bose-Einstein condensate in a rapidly rotating non-symmetric trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional harmonic trap can be described with the lowest Landau-level set of single-particle states. The condensate wave function psi(x,y) is a Gaussian exp(-r^2/2), multiplied by an analytic function f(z) of the complex variable z= x+ i y. The criterion for a quantum phase transition to a non-superfluid correlated many-body state is usually expressed in terms of the ratio of the number of particles to the number of vortices. Here, a similar description applies to a rapidly rotating non-symmetric two-dimensional trap with arbitrary quadratic anisotropy (omega_x^2 < omega_y^2). The corresponding condensate wave function psi(x,y) is a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function f(z), where z = x + i \beta_- y is a stretched complex variable and 0< \beta_- <1 is a real parameter that depends on the trap anisotropy and the rotation frequency. Both in the mean-field Thomas-Fermi approximation and in the mean-field lowest Landau level approximation with many visible vortices, an anisotropic parabolic density profile minimizes the energy. An elongated condensate grows along the soft trap direction yet ultimately shrinks along the tight trap direction. The criterion for the quantum phase transition to a correlated state is generalized (1) in terms of N/L_z, which suggests that a non-symmetric trap should make it easier to observe this transition or (2) in terms of a "fragmented" correlated state, which suggests that a non-symmetric trap should make it harder to observe this transition. An alternative scenario involves a crossover to a quasi one-dimensional condensate without visible vortices, as suggested by Aftalion et al., Phys. Rev. A 79, 011603(R) (2009).Comment: 20 page

Dynamics of vortices in weakly interacting Bose-Einstein condensates

We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.Comment: 8 pages, 7 figures, one reference updated, typos correcte

Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 + y^2, multiplied by an analytic function P(z) of the single complex variable z= x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate wave function psi(x,y) has the form of a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function P(zeta), where zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of P(zeta) again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur

Managing Opportunities and Challenges of Co-Authorship

Research with the largest impact on practice and science is often conducted by teams with diverse substantive, clinical, and methodological expertise. Team and interdisciplinary research has created authorship groups with varied expertise and expectations. Co-authorship among team members presents many opportunities and challenges. Intentional planning, clear expectations, sensitivity to differing disciplinary perspectives, attention to power differentials, effective communication, timelines, attention to published guidelines, and documentation of progress will contribute to successful co-authorship. Both novice and seasoned authors will find the strategies identified by the Western Journal of Nursing Research Editorial Board useful for building positive co-authorship experiences

Implications of a Low sin(2 beta): A Strategy for Exploring New Flavor Physics

We explore the would-be consequences of a low value of the CP-violating phase $\sin2\beta_{\psi K}$. The importance of a reference triangle obtained from measurements that are independent of $B$--$\bar B$ and $K$--$\bar K$ mixing is stressed. It can be used to extract separately potential New Physics contributions to mixing in the $B_d$, $B_s$ and $K$ systems. We discuss several constructions of this triangle, which will be feasible in the near future. The discrete ambiguity is at most two-fold and eventually can be completely removed. Simultaneously, it will be possible to probe for New Physics in loop-dominated rare decays.Comment: 9 pages, 6 figure

Gravity of higher-dimensional global defects

Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the n extra dimensions. For Lambda = 0 and n > 2, the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For Lambda > 0, one class of solutions describes spherical branes in an inflating higher-dimensional universe. Instantons obtained by a Euclidean continuation of such solutions describe quantum nucleation of the entire inflating brane-world, or of a spherical brane in an inflating higher-dimensional universe. For Lambda < 0, one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for n = 1 and by Gregory for n = 2.Comment: 18 pages, no figures, uses revte

Formats of Winning Strategies for Six Types of Pushdown Games

The solution of parity games over pushdown graphs (Walukiewicz '96) was the first step towards an effective theory of infinite-state games. It was shown that winning strategies for pushdown games can be implemented again as pushdown automata. We continue this study and investigate the connection between game presentations and winning strategies in altogether six cases of game arenas, among them realtime pushdown systems, visibly pushdown systems, and counter systems. In four cases we show by a uniform proof method that we obtain strategies implementable by the same type of pushdown machine as given in the game arena. We prove that for the two remaining cases this correspondence fails. In the conclusion we address the question of an abstract criterion that explains the results

Role of the anterior insula in task-level control and focal attention

In humans, the anterior insula (aI) has been the topic of considerable research and ascribed a vast number of functional properties by way of neuroimaging and lesion studies. Here, we argue that the aI, at least in part, plays a role in domain-general attentional control and highlight studies (Dosenbach et al. 2006; Dosenbach et al. 2007) supporting this view. Additionally, we discuss a study (Ploran et al. 2007) that implicates aI in processes related to the capture of focal attention. Task-level control and focal attention may or may not reflect information processing supported by a single functional area (within the aI). Therefore, we apply a novel technique (Cohen et al. 2008) that utilizes resting state functional connectivity MRI (rs-fcMRI) to determine whether separable regions exist within the aI. rs-fcMRI mapping suggests that the ventral portion of the aI is distinguishable from more dorsal/anterior regions, which are themselves distinct from more posterior parts of the aI. When these regions are applied to functional MRI (fMRI) data, the ventral and dorsal/anterior regions support processes potentially related to both task-level control and focal attention, whereas the more posterior aI regions did not. These findings suggest that there exists some functional heterogeneity within aI that may subserve related but distinct types of higher-order cognitive processing