Self Similar Spherical Collapse Revisited: a Comparison between Gas and Dark Matter Dynamics

We reconsider the collapse of cosmic structures in an Einstein-de Sitter Universe, using the self similar initial conditions of Fillmore & Goldreich (1984). We first derive a new approximation to describe the dark matter dynamics in spherical geometry, that we refer to the "fluid approach". This method enables us to recover the self-similarity solutions of Fillmore & Goldreich for dark matter. We derive also new self-similarity solutions for the gas. We thus compare directly gas and dark matter dynamics, focusing on the differences due to their different dimensionalities in velocity space. This work may have interesting consequences for gas and dark matter distributions in large galaxy clusters, allowing to explain why the total mass profile is always steeper than the X-ray gas profile. We discuss also the shape of the dark matter density profile found in N-body simulations in terms of a change of dimensionality in the dark matter velocity space. The stable clustering hypothesis has been finally considered in the light of this analytical approach.Comment: 14 pages, 2 figures, accepted for publication in The Astrophysical Journa

A Generalization of Haldane state-counting procedure and π\pi-deformations of statistics

We consider the generalization of Haldane's state-counting procedure to describe all possible types of exclusion statistics which are linear in the deformation parameter $g$. The statistics are parametrized by elements of the symmetric group of the particles in question. For several specific cases we determine the form of the distribution functions which generalizes results obtained by Wu. Using them we analyze the low-temperature behavior and thermodynamic properties of these systems and compare our results with previous studies of the thermodynamics of a gas of $g$-ons. Various possible physical applications of these constructions are discussed.Comment: 17 pages, latex, 6 figures small corrections were made, reference and acknowledgments are adde

Exact vortex nucleation and cooperative vortex tunneling in dilute BECs

With the imminent advent of mesoscopic rotating BECs in the lowest Landau level (LLL) regime, we explore LLL vortex nucleation. An exact many-body analysis is presented in a weakly elliptical trap for up to 400 particles. Striking non-mean field features are exposed at filling factors >>1 . Eg near the critical rotation frequency pairs of energy levels approach each other with exponential accuracy. A physical interpretation is provided by requantising a mean field theory, where 1/N plays the role of Planck's constant, revealing two vortices cooperatively tunneling between classically degenerate energy minima. The tunnel splitting variation is described in terms of frequency, particle number and ellipticity.Comment: 4 pages,4 figure

Anomalous hydrodynamics and "normal" fluids in rapidly rotating BECs

In rapidly rotating bose systems we show that there is a region of anomalous hydrodynamics whilst the system is still condensed, which coincides with the mean field quantum Hall regime. An immediate consequence is the absence of a normal fluid in any conventional sense. However, even the superfluid hydrodynamics is not described by conventional Bernoulli and continuity equations. We show there are kinematic constraints which connect spatial variations of density and phase, that the positions of vortices are not the simplest description of the dynamics of such a fluid (despite their utility in describing the instantaneous state of the condensate) and that the most compact description allows solution of some illuminating examples of motion. We demonstrate, inter alia, a very simple relation between vortices and surface waves. We show the surface waves can form a "normal fluid" which absorbs energy and angular momentum from vortex motion in the trap. The time scale of this process is sensitive to the initial configuration of the vortices, which can lead to long-lived vortex patches - perhaps related to those observed at JILA.Comment: 4 pages; 1 sentence and references modifie