16,902 research outputs found
Perturbation Theory around Non-Nested Fermi Surfaces I. Keeping the Fermi Surface Fixed
The perturbation expansion for a general class of many-fermion systems with a
non-nested, non-spherical Fermi surface is renormalized to all orders. In the
limit as the infrared cutoff is removed, the counterterms converge to a finite
limit which is differentiable in the band structure. The map from the
renormalized to the bare band structure is shown to be locally injective. A new
classification of graphs as overlapping or non-overlapping is given, and
improved power counting bounds are derived from it. They imply that the only
subgraphs that can generate factorials in the order of the
renormalized perturbation series are indeed the ladder graphs and thus give a
precise sense to the statement that `ladders are the most divergent diagrams'.
Our results apply directly to the Hubbard model at any filling except for
half-filling. The half-filled Hubbard model is treated in another place.Comment: plain TeX with postscript figures in a uuencoded gz-compressed tar
file. Put it on a separate directory before unpacking, since it contains
about 40 files. If you have problems, requests or comments, send e-mail to
[email protected]
A Proof of Luttinger Theorem
A rigorous and simple perturbative proof of Luttinger's theorem is sketched
for Fermi liquids in two and three dimensions. It is proved that in the finite
volume, the quasi-particle density is independent of the interaction strength.
The thermodynamic limit is then controlled to all orders in perturbation
theory.Comment: 7 page
Streaming velocities as a dynamical estimator of Omega
It is well known that estimating the pairwise velocity of galaxies, v_{12},
from the redshift space galaxy correlation function is difficult because this
method is highly sensitive to the assumed model of the pairwise velocity
dispersion. Here we propose an alternative method to estimate v_{12} directly
from peculiar velocity samples, which contain redshift-independent distances as
well as galaxy redshifts. In contrast to other dynamical measures which
determine beta = sigma_8 x Omega^{0.6}, our method can provide an estimate of
(sigma_8)^2 x Omega^{0.6} for a range of sigma_8 (here Omega is the
cosmological mass density parameter while sigma_8 is the standard normalization
parameter for the spectrum of matter density fluctuations). We demonstrate how
to measure this quantity from realistic catalogues.Comment: 8 pages of text, 4 figures Subject headings: Cosmology: theory -
observation - peculiar velocities: large scale flows Last name of one of the
authors was misspelled. It is now corrected. Otherwise the manuscript is
identical to its original versio
Evidence for a low-density Universe from the relative velocities of galaxies
The motions of galaxies can be used to constrain the cosmological density
parameter Omega and the clustering amplitude of matter on large scales. The
mean relative velocity of galaxy pairs, estimated from the Mark III survey,
indicates that Omega = 0.35 +0.35/-0.25. If the clustering of galaxies is
unbiased on large scales, Omega = 0.35 +/- 0.15, so that an unbiased
Einstein-de Sitter model (Omega = 1) is inconsistent with the data.Comment: 12 pages, 2 figures, to appear in the Jan.7 issue of ``Science''; In
the original version, the title appeared twice. This problem has now been
corrected. No other changes were mad
Measuring Omega with Galaxy Streaming Velocities
The mean pairwise velocity of galaxies has traditionally been estimated from
the redshift space galaxy correlation function. This method is notorious for
being highly sensitive to the assumed model of the pairwise velocity
dispersion. Here we propose an alternative method to estimate the streaming
velocity directly from peculiar velocity samples, which contain
redshift-independent distances as well as galaxy redshifts. This method can
provide an estimate of for a range of where
is the cosmological density parameter, while is the
standard normalization for the power spectrum of density fluctuations. We
demonstrate how to measure this quantity from realistic catalogues and identify
the main sources of bias and errorsComment: Proceedings of New Worlds in Astroparticle Physics, 6 pages, 2
figure
Lunar Resource Assessment: an Industry Perspective
The goals of the U.S. space program are to return to the Moon, establish a base, and continue onward to Mars. To accomplish this in a relatively short time frame and to avoid the high costs of transporting materials from the Earth, resources on the Moon will need to be mined. Oxygen will be one of the most important resources, to be used as a rocket propellant and for life support. Ilmenite and lunar regolith have both been considered as ores for the production of oxygen. Resource production on the Moon will be a very important part of the U.S. space program. To produce resources we must explore to identify the location of ore or feedback and calculate the surface and underground reserves. Preliminary resource production tests will provide the information that can be used in final plant design. Bechtel Corporation's experience in terrestrial engineering and construction has led to an interest in lunar resource assessment leading to the construction of production facilities on the Moon. There is an intimate link between adequate resource assessment to define feedstock quantity and quality, material processing requirements, and the successful production of lunar oxygen. Although lunar resource assessment is often viewed as a research process, the engineering and production aspects are very important to consider. Resource production often requires the acquisition of different types, scales, or resolutions of data than that needed for research, and it is needed early in the exploration process. An adequate assessment of the grade, areal extent, and depth distribution of the resources is a prerequisite to mining. The need for a satisfactory resource exploration program using remote sensing techniques, field sampling, and chemical and physical analysis is emphasized. These data can be used to define the ore for oxygen production and the mining, processing facilities, and equipment required
Water production models for Comet Bradfield (1979 l)
The IUE observations of Comet Bradfield (1979 l) made 10 January 1980 to 3 March 1980 permit a detailed study of water production for this comet. Brightness measurements are presented for all three water dissociation products, H, O, and OH, and comparisons are made with model predictions. The heliocentric variation of the water production rate was derived
THE WAIT-AND-SEE OPTION IN ASCENDING PRICE AUCTIONS
Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible
resource) and assigning the resulting portions to several players in a way that
each of the players feels to have received a ``fair'' amount of the cake. An
important notion of fairness is envy-freeness: No player wishes to switch the
portion of the cake received with another player's portion. Despite intense
efforts in the past, it is still an open question whether there is a
\emph{finite bounded} envy-free cake-cutting protocol for an arbitrary number
of players, and even for four players. We introduce the notion of degree of
guaranteed envy-freeness (DGEF) as a measure of how good a cake-cutting
protocol can approximate the ideal of envy-freeness while keeping the protocol
finite bounded (trading being disregarded). We propose a new finite bounded
proportional protocol for any number n \geq 3 of players, and show that this
protocol has a DGEF of 1 + \lceil (n^2)/2 \rceil. This is the currently best
DGEF among known finite bounded cake-cutting protocols for an arbitrary number
of players. We will make the case that improving the DGEF even further is a
tough challenge, and determine, for comparison, the DGEF of selected known
finite bounded cake-cutting protocols.Comment: 37 pages, 4 figure
Linear semigroups with coarsely dense orbits
Let be a finitely generated abelian semigroup of invertible linear
operators on a finite dimensional real or complex vector space . We show
that every coarsely dense orbit of is actually dense in . More
generally, if the orbit contains a coarsely dense subset of some open cone
in then the closure of the orbit contains the closure of . In the
complex case the orbit is then actually dense in . For the real case we give
precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page
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