RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model

We relate the Z$_2$ gauge theory formalism of the Kitaev model to the SU(2) gauge theory of the resonating valence bond (RVB) physics. Further, we reformulate a known Jordan-Wigner transformation of Kitaev model on a torus in a general way that shows that it can be thought of as a Z$_2$ gauge fixing procedure. The conserved quantities simplify in terms of the gauge invariant Jordan-Wigner fermions, enabling us to construct exact eigen states and calculate physical quantities. We calculate the fermionic spectrum for flux free sector for different gauge field configurations and show that the ground state is four-fold degenerate on a torus in thermodynamic limit. Further on a torus we construct four mutually anti-commuting operators which enable us to prove that all eigenstates of this model are four fold degenerate in thermodynamic limit.Comment: 12 pages, 3 figures. Added affiliation and a new section, 'Acknowledgements'.Typos correcte

Galaxy size trends as a consequence of cosmology

We show that recently documented trends in galaxy sizes with mass and redshift can be understood in terms of the influence of underlying cosmic evolution; a holistic view which is complimentary to interpretations involving the accumulation of discreet evolutionary processes acting on individual objects. Using standard cosmology theory, supported with results from the Millennium simulations, we derive expected size trends for collapsed cosmic structures, emphasising the important distinction between these trends and the assembly paths of individual regions. We then argue that the observed variation in the stellar mass content of these structures can be understood to first order in terms of natural limitations of cooling and feedback. But whilst these relative masses vary by orders of magnitude, galaxy and host radii have been found to correlate linearly. We explain how these two aspects will lead to galaxy sizes that closely follow observed trends and their evolution, comparing directly with the COSMOS and SDSS surveys. Thus we conclude that the observed minimum radius for galaxies, the evolving trend in size as a function of mass for intermediate systems, and the observed increase in the sizes of massive galaxies, may all be considered an emergent consequence of the cosmic expansion.Comment: 14 pages, 13 figures. Accepted by MNRA

A Physical Model for Co-evolution of QSOs and of their Spheroidal Hosts

At variance with most semi-analytic models, in the Anti-hierarchical Baryon Collapse scenario (Granato et al. 2001, 2004) the main driver of the galaxy formation and evolution is not the merging sequence but are baryon processes. This approach emphasizes, still in the framework of the hierarchical clustering paradigm for dark matter halos, feedback processes from supernova explosions and from active nuclei, that tie together star formation in spheroidal galaxies and the growth of black holes at their centers. We review some recent results showing the remarkably successful predictive power of this scenario, which allows us to account for the evolution with cosmic time of a broad variety of properties of galaxies and active nuclei, which proved to be very challenging for competing models.Comment: Invited talk at the Specola Vaticana Workshop on "AGN and Galaxy Evolution", Castel Gandolfo, 3-6 October 2005, 10 pages, 2 figure

From First Galaxies to QSOs: feeding the baby monsters

We present a physical model for the coevolution of massive spheroidal galaxies and active nuclei at their centers. Supernova heating is increasingly effective in slowing down the star formation and in driving gas outflows in smaller and smaller dark matter halos. Thus the more massive protogalaxies virializing at early times are the sites of faster star formation. The correspondingly higher radiation drag causes a faster angular momentum loss by the gas and induces a larger accretion rate onto the central black hole. In turn, the kinetic energy of the outflows powered by the active nuclei can unbind the residual gas in a time shorter for larger halos. The model accounts for a broad variety of dynamical, photometric and metallicity properties of early-type galaxies, for the M_BH -- \sigma relation and for the local supermassive black-hole mass function.Comment: 6 pages, contributed paper to Proceedings of the Conference on "Growing Black Holes" held in Garching, Germany, on June 21-25, 2004, edited by A. Merloni, S. Nayakshin and R. Sunyaev, Springer-Verlag series of "ESO Astrophysics Symposia

Exact solution of a 2d random Ising model

The model considered is a d=2 layered random Ising system on a square lattice with nearest neighbours interaction. It is assumed that all the vertical couplings are equal and take the positive value J while the horizontal couplings are quenched random variables which are equal in the same row but can take the two possible values J and J-K in different rows. The exact solution is obtained in the limit case of infinite K for any distribution of the horizontal couplings. The model which corresponds to this limit can be seen as an ordinary Ising system where the spins of some rows, chosen at random, are frozen in an antiferromagnetic order. No phase transition is found if the horizontal couplings are independent random variables while for correlated disorder one finds a low temperature phase with some glassy properties.Comment: 10 pages, Plain TeX, 3 ps figures, submitted to Europhys. Let

The Allometry of Daily Energy Expenditure in Hummingbirds: An Energy Budget Approach

1. Within-clade allometric relationships represent standard laws of scaling between energy and size, and their outliers provide new avenues for physiological and ecological research. According to the metabolic-level boundaries hypothesis, metabolic rates as a function of mass are expected to scale closer to 0.67 when driven by surface-related processes (e.g. heat or water flux), while volume-related processes (e.g. activity) generate slopes closer to one. 2. In birds, daily energy expenditure (DEE) scales with body mass (M) in the relationship log (DEE)=2.35+0.68×log (M), consistent with surface-level processes driving the relationship. However, taxon-specific patterns differ from the scaling slope of all birds. 3. Hummingbirds have the highest mass-specific metabolic rates among all vertebrates. Previous studies on a few hummingbird species, without accounting for the phylogeny, estimated that the DEE–body mass relationship for hummingbirds was log (DEE)=1.72+1.21×log (M). In Contrast to the theoretical expectations, this slope \u3e1 indicates that larger hummingbirds are less metabolically efficient than smaller hummingbirds. 4. We collected DEE and mass data for 12 hummingbird species, which, combined with published data, represented 17 hummingbird species in eight of nine hummingbird clades over a sixfold size range of body size (2.7–17.5 g). 5. After accounting for phylogenetic relatedness, we found DEE scales with body mass as log(DEE)=2.04+0.95×log (M). This slope of 0.95 is lower than previously estimated for hummingbirds, but much higher than the slope for all birds (0.68). The high slopes of torpor, hovering and flight potentially explain the high interspecific DEE slope for hummingbirds compared to other endotherms

Knots in a Spinor Bose-Einstein Condensate

We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.Comment: 4 pages, 3 figure

Exact results for spin dynamics and fractionization in the Kitaev Model

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in non-trivial quantum spin models. The result is also novel: in spite of presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation, showing existence of a gapless but short range spin liquid. An unusual, \emph{all energy scale fractionization}of a spin -flip quanta, into two infinitely massive $\pi$-fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.Comment: 4 pages, 2 figures. Typose corrected, figure made better, clarifying statements and references adde

Occupation of X-ray selected galaxy groups by X-ray AGN

We present the first direct measurement of the mean Halo Occupation Distribution (HOD) of X-ray selected AGN in the COSMOS field at z < 1, based on the association of 41 XMM and 17 C-COSMOS AGN with member galaxies of 189 X-ray detected galaxy groups from XMM and Chandra data. We model the mean AGN occupation in the halo mass range logM_200[Msun] = 13-14.5 with a rolling-off power-law with the best fit index alpha = 0.06(-0.22;0.36) and normalization parameter f_a = 0.05(0.04;0.06). We find the mean HOD of AGN among central galaxies to be modelled by a softened step function at logMh > logMmin = 12.75 (12.10,12.95) Msun while for the satellite AGN HOD we find a preference for an increasing AGN fraction with Mh suggesting that the average number of AGN in satellite galaxies grows slower (alpha_s < 0.6) than the linear proportion (alpha_s = 1) observed for the satellite HOD of samples of galaxies. We present an estimate of the projected auto correlation function (ACF) of galaxy groups over the range of r_p = 0.1-40 Mpc/h at = 0.5. We use the large-scale clustering signal to verify the agreement between the group bias estimated by using the observed galaxy groups ACF and the value derived from the group mass estimates. We perform a measurement of the projected AGN-galaxy group cross-correlation function, excluding from the analysis AGN that are within galaxy groups and we model the 2-halo term of the clustering signal with the mean AGN HOD based on our results.Comment: Accepted for publication in The Astrophysical Journa