Anyonic Excitations in Fast Rotating Bose Gases Revisited

The role of anyonic excitations in fast rotating harmonically trapped Bose gases in a fractional Quantum Hall state is examined. Standard Chern-Simons anyons as well as "non standard" anyons obtained from a statistical interaction having Maxwell-Chern-Simons dynamics and suitable non minimal coupling to matter are considered. Their respective ability to stabilize attractive Bose gases under fast rotation in the thermodynamical limit is studied. Stability can be obtained for standard anyons while for non standard anyons, stability requires that the range of the corresponding statistical interaction does not exceed the typical wavelenght of the atoms.Comment: 5 pages. Improved version to be published in Phys. Rev. A, including a physical discussion on relevant interactions and scattering regime together with implication on the nature of statistical interactio

Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.Comment: 21 pages, 4 color figure

Generalized exclusion and Hopf algebras

We propose a generalized oscillator algebra at the roots of unity with generalized exclusion and we investigate the braided Hopf structure. We find that there are two solutions: these are the generalized exclusions of the bosonic and fermionic types. We also discuss the covariance properties of these oscillatorsComment: 10 pages, to appear in J. Phys.

N=1 gauge superpotentials from supergravity

We review the supergravity derivation of some non-perturbatively generated effective superpotentials for N=1 gauge theories. Specifically, we derive the Veneziano-Yankielowicz superpotential for pure N=1 Super Yang-Mills theory from the warped deformed conifold solution, and the Affleck-Dine-Seiberg superpotential for N=1 SQCD from a solution describing fractional D3-branes on a C^3 / Z_2 x Z_2 orbifold.Comment: LaTeX, iopart class, 8 pages, 3 figures. Contribution to the proceedings of the workshop of the RTN Network "The quantum structure of space-time and the geometric nature of fundamental interactions", Copenhagen, September 2003; v2: published version with minor clarification

Statistics of Q-Oscillators, Quons and Relation to Fractional Satistics

The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic $q$-oscillators are found for their corresponding Fock space representations in the case when the hamiltonian is identified with the number operator. In this case and for nonrelativistic particles, the single-particle temperature Green function is defined with $q$-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic $q$-gases in an arbitrary space dimension are found near Bose statistics, as well as the one for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated. The phenomenon of Bose-Einstein condensation in the $q$-deformed gases is also discussed.Comment: 21 pages, Latex, HU-TFT-93-2

Gravitational anomaly and fundamental forces

I present an argument, based on the topology of the universe, why there are three generations of fermions. The argument implies a preferred gauge group of SU(5), but with SO(10) representations of the fermions. The breaking pattern SU(5) to SU(3)xSU(2)xU(1) is preferred over the pattern SU(5) to SU(4)xU(1). On the basis of the argument one expects an asymmetry in the early universe microwave data, which might have been detected already.Comment: Contribution to the 2nd School and Workshop on Quantum Gravity and Quantum Geometry. Corfu, september 13-20 2009. 10 page

From the Chern-Simons theory for the fractional quantum Hall effect to the Luttinger model of its edges

The chiral Luttinger model for the edges of the fractional quantum Hall effect is obtained as the low energy limit of the Chern-Simons theory for the two dimensional system. In particular we recover the Kac-Moody algebra for the creation and annihilation operators of the edge density waves and the bosonization formula for the electronic operator at the edge.Comment: 4 pages, LaTeX, 1 Postscript figure include

The 2+1 Kepler Problem and Its Quantization

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass frame. When the system is quantized, we find some possibly general effects of quantum gravity, such as a minimal distances and a foaminess of the spacetime at the order of the Planck length. We also obtain a quantization of geometry, which restricts the possible asymptotic geometries of the universe.Comment: 59 pages, LaTeX2e, 9 eps figure

Supergravity p-branes revisited: extra parameters, uniqueness, and topological censorship

We perform a complete integration of the Einstein-dilaton-antisymmetric form action describing black p-branes in arbitrary dimensions assuming the transverse space to be homogeneous and possessing spherical, toroidal or hyperbolic topology. The generic solution contains eight parameters satisfying one constraint. Asymptotically flat solutions form a five-parametric subspace, while conditions of regularity of the non-degenerate event horizon further restrict this number to three, which can be related to the mass and the charge densities and the asymptotic value of the dilaton. In the case of a degenerate horizon, this number is reduced by one. Our derivation constitutes a constructive proof of the uniqueness theorem for $p$-branes with the homogeneous transverse space. No asymptotically flat solutions with toroidal or hyperbolic transverse space within the considered class are shown to exist, which result can be viewed as a demonstration of the topological censorship for p-branes. From our considerations it follows, in particular, that some previously discussed p-brane-like solutions with extra parameters do not satisfy the standard conditions of asymptotic flatness and absence of naked singularities. We also explore the same system in presence of a cosmological constant, and derive a complete analytic solution for higher-dimensional charged topological black holes, thus proving their uniqueness.Comment: Revtex4, no figure

Generalizations of entanglement based on coherent states and convex sets

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our original motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.Comment: 37 page