60,672 research outputs found
Maximal entropy random networks with given degree distribution
Using a maximum entropy principle to assign a statistical weight to any
graph, we introduce a model of random graphs with arbitrary degree distribution
in the framework of standard statistical mechanics. We compute the free energy
and the distribution of connected components. We determine the size of the
percolation cluster above the percolation threshold. The conditional degree
distribution on the percolation cluster is also given. We briefly present the
analogous discussion for oriented graphs, giving for example the percolation
criterion.Comment: 22 pages, LateX, no figur
A lunar base for SETI (Search for Extraterrestrial Intelligence)
The possibilities of using lanar based radio antennas in search of intelligent extraterrestrial communications is explored. The proposed NASA search will have two search modes: (1) An all sky survey covering the frequency range from 1 to 10 GHz; and (2) A high sensitivity targeted search listening for signals from the approx. 800 solar type stars within 80 light years of the Sun, and covering 1 to 3 GHz
A Lattice Study of the Gluon Propagator in Momentum Space
We consider pure glue QCD at beta=5.7, beta=6.0 and beta=6.3. We evaluate the
gluon propagator both in time at zero 3-momentum and in momentum space. From
the former quantity we obtain evidence for a dynamically generated effective
mass, which at beta=6.0 and beta=6.3 increases with the time separation of the
sources, in agreement with earlier results. The momentum space propagator G(k)
provides further evidence for mass generation. In particular, at beta=6.0, for
k less than 1 GeV, the propagator G(k) can be fit to a continuum formula
proposed by Gribov and others, which contains a mass scale b, presumably
related to the hadronization mass scale. For higher momenta Gribov's model no
longer provides a good fit, as G(k) tends rather to follow an inverse power
law. The results at beta=6.3 are consistent with those at beta=6.0, but only
the high momentum region is accessible on this lattice. We find b in the range
of three to four hundred MeV and the exponent of the inverse power law about
2.7. On the other hand, at beta=5.7 (where we can only study momenta up to 1
GeV) G(k) is best fit to a simple massive boson propagator with mass m. We
argue that such a discrepancy may be related to a lack of scaling for low
momenta at beta=5.7. {}From our results, the study of correlation functions in
momentum space looks promising, especially because the data points in Fourier
space turn out to be much less correlated than in real space.Comment: 19 pages + 12 uuencoded PostScript picture
Modular Invariant of Quantum Tori II: The Golden Mean
In our first article in this series ("Modular Invariant of Quantum Tori I:
Definitions Nonstandard and Standard" arXiv:0909.0143) a modular invariant of
quantum tori was defined. In this paper, we consider the case of the quantum
torus associated to the golden mean. We show that the modular invariant is
approximately 9538.249655644 by producing an explicit formula for it involving
weighted versions of the Rogers-Ramanujan functions
A 0-dimensional counter-example to rooting?
We provide an example of a 0-dimensional field theory where rooting does not
work.Comment: 3 pages; Physics Letters B (2010
Lattice results for the decay constant of heavy-light vector mesons
We compute the leptonic decay constants of heavy-light vector mesons in the
quenched approximation. The reliability of lattice computations for heavy
quarks is checked by comparing the ratio of vector to pseudoscalar decay
constant with the prediction of Heavy Quark Effective Theory in the limit of
infinitely heavy quark mass. Good agreement is found. We then calculate the
decay constant ratio for B mesons: .
We also quote quenched MeV.Comment: 11 pages, 3 postscript figs., revtex; two references adde
Dipolar SLEs
We present basic properties of Dipolar SLEs, a new version of stochastic
Loewner evolutions (SLE) in which the critical interfaces end randomly on an
interval of the boundary of a planar domain. We present a general argument
explaining why correlation functions of models of statistical mechanics are
expected to be martingales and we give a relation between dipolar SLEs and
CFTs. We compute SLE excursion and/or visiting probabilities, including the
probability for a point to be on the left/right of the SLE trace or that to be
inside the SLE hull. These functions, which turn out to be harmonic, have a
simple CFT interpretation. We also present numerical simulations of the
ferromagnetic Ising interface that confirm both the probabilistic approach and
the CFT mapping.Comment: 22 pages, 4 figure
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