11,162 research outputs found
The statistical mechanics of multi-index matching problems with site disorder
We study the statistical mechanics of multi-index matching problems where the
quenched disorder is a geometric site disorder rather than a link disorder. A
recently developed functional formalism is exploited which yields exact results
in the finite temperature thermodynamic limit. Particular attention is paid to
the zero temperature limit of maximal matching problems where the method allows
us to obtain the average value of the optimal match and also sheds light on the
algorithmic heuristics leading to that optimal matchComment: 11 pages 11 figures, RevTe
Black hole determinants and quasinormal modes
We derive an expression for functional determinants in thermal spacetimes as
a product over the corresponding quasinormal modes. As simple applications we
give efficient computations of scalar determinants in thermal AdS, BTZ black
hole and de Sitter spacetimes. We emphasize the conceptual utility of our
formula for discussing `1/N' corrections to strongly coupled field theories via
the holographic correspondence.Comment: 28 pages. v2: slightly improved exposition, references adde
Cosmic microwave background anisotropies in multi-connected flat spaces
This article investigates the signature of the seventeen multi-connected flat
spaces in cosmic microwave background (CMB) maps. For each such space it
recalls a fundamental domain and a set of generating matrices, and then goes on
to find an orthonormal basis for the set of eigenmodes of the Laplace operator
on that space. The basis eigenmodes are expressed as linear combinations of
eigenmodes of the simply connected Euclidean space. A preceding work, which
provides a general method for implementing multi-connected topologies in
standard CMB codes, is then applied to simulate CMB maps and angular power
spectra for each space. Unlike in the 3-torus, the results in most
multi-connected flat spaces depend on the location of the observer. This effect
is discussed in detail. In particular, it is shown that the correlated circles
on a CMB map are generically not back-to-back, so that negative search of
back-to-back circles in the WMAP data does not exclude a vast majority of flat
or nearly flat topologies.Comment: 33 pages, 19 figures, 1 table. Submitted to PR
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS black holes
We present a holographic derivation of the entropy of supersymmetric
asymptotically AdS black holes. We define a BPS limit of black hole
thermodynamics by first focussing on a supersymmetric family of complexified
solutions and then reaching extremality. We show that in this limit the black
hole entropy is the Legendre transform of the on-shell gravitational action
with respect to three chemical potentials subject to a constraint. This
constraint follows from supersymmetry and regularity in the Euclidean bulk
geometry. Further, we calculate, using localization, the exact partition
function of the dual SCFT on a twisted with
complexified chemical potentials obeying this constraint. This defines a
generalization of the supersymmetric Casimir energy, whose Legendre transform
at large exactly reproduces the Bekenstein-Hawking entropy of the black
hole.Comment: v4: minor changes, version published in JHE
A fingerprint based metric for measuring similarities of crystalline structures
Measuring similarities/dissimilarities between atomic structures is important
for the exploration of potential energy landscapes. However, the cell vectors
together with the coordinates of the atoms, which are generally used to
describe periodic systems, are quantities not suitable as fingerprints to
distinguish structures. Based on a characterization of the local environment of
all atoms in a cell we introduce crystal fingerprints that can be calculated
easily and allow to define configurational distances between crystalline
structures that satisfy the mathematical properties of a metric. This distance
between two configurations is a measure of their similarity/dissimilarity and
it allows in particular to distinguish structures. The new method is an useful
tool within various energy landscape exploration schemes, such as minima
hopping, random search, swarm intelligence algorithms and high-throughput
screenings
- …