109,987 research outputs found
RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model
We relate the Z 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 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
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
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 -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
Renormalization Group Approach to Strong-Coupled Superconductors
We develop an asymptotically exact renormalization group (RG) approach that
treats electron-electron and electron-phonon interactions on equal footing. The
approach allows an unbiased study of the instabilities of Fermi liquids without
the assumption of a broken symmetry. We apply our method to the problem of
strongly coupled superconductors and find the temperature T* below which the
high-temperature Fermi liquid state becomes unstable towards Cooper pairing. We
show that T* is the same as the critical temperature Tc obtained in
Eliashberg's strong coupling theory starting from the low-temperature
superconducting phase. We also show that Migdal's theorem is implicit in our
approach. Finally, our results lead to a novel way to calculate numerically,
from microscopic parameters, the transition temperature of superconductors.Comment: 6 pages, 3 figures, expanded presentation, final versio
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
The cosmic growth of the active black hole population at 1<z<2 in zCOSMOS, VVDS and SDSS
We present a census of the active black hole population at 1<z<2, by
constructing the bivariate distribution function of black hole mass and
Eddington ratio, employing a maximum likelihood fitting technique. The study of
the active black hole mass function (BHMF) and the Eddington ratio distribution
function (ERDF) allows us to clearly disentangle the active galactic nuclei
(AGN) downsizing phenomenon, present in the AGN luminosity function, into its
physical processes of black hole mass downsizing and accretion rate evolution.
We are utilizing type-1 AGN samples from three optical surveys (VVDS, zCOSMOS
and SDSS), that cover a wide range of 3 dex in luminosity over our redshift
interval of interest. We investigate the cosmic evolution of the AGN population
as a function of AGN luminosity, black hole mass and accretion rate. Compared
to z = 0, we find a distinct change in the shape of the BHMF and the ERDF,
consistent with downsizing in black hole mass. The active fraction or duty
cycle of type-1 AGN at z~1.5 is almost flat as a function of black hole mass,
while it shows a strong decrease with increasing mass at z=0. We are witnessing
a phase of intense black hole growth, which is largely driven by the onset of
AGN activity in massive black holes towards z=2. We finally compare our results
to numerical simulations and semi-empirical models and while we find reasonable
agreement over certain parameter ranges, we highlight the need to refine these
models in order to match our observations.Comment: 31 pages, 28 figures, accepted for publication in MNRA
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 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
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