Particle Yields and Ratios within Equilibrium and Non-Equilibrium Statistics

In characterizing the yields and ratios various of well identified particles in the ALICE experiment, we utilize extensive {\it additive} thermal approaches, to which various missing states of the hadron resonances are taken into consideration, as well. Despite some non-equilibrium conditions that are slightly driving this statistical approach away from equilibrium, the approaches are and remain additive and extensive. Besides van der Waals repulsive interactions (assuming that the gas constituents are no longer point-like, i.e. finite-volume corrections taken into consideration), finite pion chemical potentials as well as perturbations to the light and strange quark occupation factors are taken into account. When confronting our calculations to the ALICE measurements, we conclude that the proposed conditions for various aspects deriving the system out of equilibrium notably improve the reproduction of the experimental results, i.e. improving the statistical fits, especially the finite pion chemical potential. This points out to the great role that the non-equilibrium pion production would play, and the contributions that the hadron resonance missing states come up with, even when the principles of statistical extensivity and additivity aren't violated. These results seem to propose revising the conclusions propagated by most of the field, that the produced particles quickly reach a state of local equilibrium leading to a collective expansion often described by fluid dynamics. This situation seems not remaining restrictively valid, at very large collision energies.Comment: 15 pages, 4 figures, submitted to EP

Dynamical evolution of a doubly-quantized vortex imprinted in a Bose-Einstein Condensate

The recent experiment by Y. Shin \emph{et al.} [Phys. Rev. Lett. \textbf{93}, 160406 (2004)] on the decay of a doubly quantized vortex imprinted in $^{23}$Na condensates is analyzed by numerically solving the Gross-Pitaevskii equation. Our results, which are in very good quantitative agreement with the experiment, demonstrate that the vortex decay is mainly a consequence of dynamical instability. Despite apparent contradictions, the local density approach is consistent with the experimental results. The monotonic increase observed in the vortex lifetimes is a consequence of the fact that, for large condensates, the measured lifetimes incorporate the time it takes for the initial perturbation to reach the central slice. When considered locally, the splitting occurs approximately at the same time in every condensate, regardless of its size.Comment: 5 pages, 4 figure

Incompressible liquid state of rapidly-rotating bosons at filling factor 3/2

Bosons in the lowest Landau level, such as rapidly-rotating cold trapped atoms, are investigated numerically in the specially interesting case in which the filling factor (ratio of particle number to vortex number) is 3/2. When a moderate amount of a longer-range (e.g. dipolar) interaction is included, we find clear evidence that the ground state is in a phase constructed earlier by two of us, in which excitations possess non-Abelian statistics.Comment: 5 pages, 5 figure

Extensive/nonextensive statistics for pTp_T distributions of various charged particles produced in p+p and A+A collisions in a wide range of energies

We present a systematic study for the statistical fits of the transverse momentum distributions of charged pions, Kaons and protons produced at energies ranging between 7.7 and 2670 GeV to the extensive Boltzmann-Gibbs (BG) and the nonextensive statistics (Tsallis as a special type and the generic axiomatic nonextensive approach). We also present a comprehensive review on various experimental parametrizations proposed to fit the transverse momentum distributions of these produced particles. The inconsistency that the BG approach is to be utilized in characterizing the chemical freezeout, while the Tsallis approach in determining the kinetic freezeout is elaborated. The resulting energy dependence of the different fit parameters largely varies with the particle species and the degree of (non)extensivity. This manifests that the Tsallis nonextensive approach seems to work well for p+p rather than for A+A collisions. Drawing a complete picture of the utilization of Tsallis statistics in modeling the transverse momentum distributions of several charged particle produced at a wide range of energies and accordingly either disprove or though confirm the relevant works are main advantages of this review. We propose analytical expressions for the dependence of the fit parameters obtained on the size of the colliding system, the energy, as well as the types of the statistical approach applied. We conclude that the statistical dependence of the various fit parameters, especially between Boltzmann and Tsallis approaches could be understood that the statistical analysis ad hoc is biased to the corresponding degree of extensivity (Boltzmann) or nonextensivity (Tsallis). Alternatively, the empirical parameterizations, the other models, and the generic (non)extensive approach seem to relax this biasness.Comment: 42 pages, 17 figures, IX tables, submitted to JSTA

Global behavior of a fourth order difference equation

We determine the forbidden set, introduce an explicit formula for the solutions, and discuss the global behavior of solutions of a fourth order difference equation

Giant vortices in combined harmonic and quartic traps

We consider a rotating Bose-Einstein condensate confined in combined harmonic and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin and J. Dalibard, cond-mat/0307464]. We investigate numerically the behavior of the wave function which solves the three-dimensional Gross Pitaevskii equation. When the harmonic part of the potential is dominant, as the angular velocities $Omega$ increases, the vortex lattice evolves into a giant vortex. We also investigate a case not covered by the experiments or the previous numerical works: for strong quartic potentials, the giant vortex is obtained for lower $Omega$, before the lattice is formed. We analyze in detail the three dimensional structure of vortices

Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime

By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure

Energy gaps and roton structure above the nu=1/2 Laughlin state of a rotating dilute Bose-Einstein condensate

Exact diagonalization study of a rotating dilute Bose-Einstein condensate reveals that as the first vortex enters the system the degeneracy of the low-energy yrast spectrum is lifted and a large energy gap emerges. As more vortices enter with faster rotation, the energy gap decreases towards zero, but eventually the spectrum exhibits a rotonlike structure above the nu=1/2 Laughlin state without having a phonon branch despite the short-range nature of the interaction.Comment: 4 pages, 4 figures, 1 tabl

Phases of a rotating Bose-Einstein condensate with anharmonic confinement

We examine an effectively repulsive Bose-Einstein condensate of atoms that rotates in a quadratic-plus-quartic potential. With use of a variational method we identify the three possible phases of the system (multiple quantization, single quantization, and a mixed phase) as a function of the rotational frequency of the gas and of the coupling constant. The derived phase diagram is shown to be universal and the continuous transitions to be exact in the limit of weak coupling and small anharmonicity. The variational results are found to be consistent with numerical solutions of the Gross-Pitaevskii equation.Comment: 8 pages, 6 figure