2,799 research outputs found
Wilson Fermions on a Randomly Triangulated Manifold
A general method of constructing the Dirac operator for a randomly
triangulated manifold is proposed. The fermion field and the spin connection
live, respectively, on the nodes and on the links of the corresponding dual
graph. The construction is carried out explicitly in 2-d, on an arbitrary
orientable manifold without boundary. It can be easily converted into a
computer code. The equivalence, on a sphere, of Majorana fermions and Ising
spins in 2-d is rederived. The method can, in principle, be extended to higher
dimensions.Comment: 18 pages, latex, 6 eps figures, fig2 corrected, Comment added in the
conclusion sectio
The Cost of Address Translation
Modern computers are not random access machines (RAMs). They have a memory
hierarchy, multiple cores, and virtual memory. In this paper, we address the
computational cost of address translation in virtual memory. Starting point for
our work is the observation that the analysis of some simple algorithms (random
scan of an array, binary search, heapsort) in either the RAM model or the EM
model (external memory model) does not correctly predict growth rates of actual
running times. We propose the VAT model (virtual address translation) to
account for the cost of address translations and analyze the algorithms
mentioned above and others in the model. The predictions agree with the
measurements. We also analyze the VAT-cost of cache-oblivious algorithms.Comment: A extended abstract of this paper was published in the proceedings of
ALENEX13, New Orleans, US
Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations
We calculate the spectral dimension for a nonperturbative lattice approach to
quantum gravity, known as causal dynamical triangulations (CDT), showing that
the dimension of spacetime smoothly decreases from approximately 4 on large
distance scales to approximately 3/2 on small distance scales. This novel
result may provide a possible resolution to a long-standing argument against
the asymptotic safety scenario. A method for determining the relative lattice
spacing within the physical phase of the CDT parameter space is also outlined,
which might prove useful when studying renormalization group flow in models of
lattice quantum gravity.Comment: 21 pages, 8 figures, 4 tables. Typos corrected, 3 tables added.
Conclusions unchanged. Conforms with version published in JHE
Eigenvalue density of empirical covariance matrix for correlated samples
We describe a method to determine the eigenvalue density of empirical
covariance matrix in the presence of correlations between samples. This is a
straightforward generalization of the method developed earlier by the authors
for uncorrelated samples. The method allows for exact determination of the
experimental spectrum for a given covariance matrix and given correlations
between samples in the limit of large N and N/T=r=const with N being the number
of degrees of freedom and T being the number of samples. We discuss the effect
of correlations on several examples.Comment: 12 pages, 5 figures, to appear in Acta Phys. Pol. B (Proceedings of
the conference on `Applications of Random Matrix Theory to Economy and Other
Complex Systems', May 25-28, 2005, Cracow, Polan
The Universe from Scratch
A fascinating and deep question about nature is what one would see if one
could probe space and time at smaller and smaller distances. Already the
19th-century founders of modern geometry contemplated the possibility that a
piece of empty space that looks completely smooth and structureless to the
naked eye might have an intricate microstructure at a much smaller scale. Our
vastly increased understanding of the physical world acquired during the 20th
century has made this a certainty. The laws of quantum theory tell us that
looking at spacetime at ever smaller scales requires ever larger energies, and,
according to Einstein's theory of general relativity, this will alter spacetime
itself: it will acquire structure in the form of "curvature". What we still
lack is a definitive Theory of Quantum Gravity to give us a detailed and
quantitative description of the highly curved and quantum-fluctuating geometry
of spacetime at this so-called Planck scale. - This article outlines a
particular approach to constructing such a theory, that of Causal Dynamical
Triangulations, and its achievements so far in deriving from first principles
why spacetime is what it is, from the tiniest realms of the quantum to the
large-scale structure of the universe.Comment: 31 pages, 5 figures; review paper commissioned by Contemporary
Physics and aimed at a wider physics audience; minor beautifications,
coincides with journal versio
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