2,509 research outputs found
Extended Uncertainty Principle for Rindler and cosmological horizons
We find exact formulas for the Extended Uncertainty Principle (EUP) for the
Rindler and Friedmann horizons and show that they can be expanded to obtain
asymptotic forms known from the previous literature. We calculate the
corrections to Hawking temperature and Bekenstein entropy of a black hole in
the universe due to Rindler and Friedmann horizons. The effect of the EUP is
similar to the canonical corrections of thermal fluctuations and so it rises
the entropy signalling further loss of information.Comment: 7 pages, 6 figures, REVTEX 4.1, minor changes, refs update
Beating the Generator-Enumeration Bound for -Group Isomorphism
We consider the group isomorphism problem: given two finite groups G and H
specified by their multiplication tables, decide if G cong H. For several
decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the
smallest prime dividing the order of the group) has been the best worst-case
result for general groups. In this work, we show the first improvement over the
generator-enumeration bound for p-groups, which are believed to be the hard
case of the group isomorphism problem. We start by giving a Turing reduction
from group isomorphism to n^((1 / 2) log_p n + O(1)) instances of p-group
composition-series isomorphism. By showing a Karp reduction from p-group
composition-series isomorphism to testing isomorphism of graphs of degree at
most p + O(1) and applying algorithms for testing isomorphism of graphs of
bounded degree, we obtain an n^(O(p)) time algorithm for p-group
composition-series isomorphism. Combining these two results yields an algorithm
for p-group isomorphism that takes at most n^((1 / 2) log_p n + O(p)) time.
This algorithm is faster than generator-enumeration when p is small and slower
when p is large. Choosing the faster algorithm based on p and n yields an upper
bound of n^((1 / 2 + o(1)) log n) for p-group isomorphism.Comment: 15 pages. This is an updated and improved version of the results for
p-groups in arXiv:1205.0642 and TR11-052 in ECC
Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs
The Graph Isomorphism problem restricted to graphs of bounded treewidth or
bounded tree distance width are known to be solvable in polynomial time
[Bod90],[YBFT99]. We give restricted space algorithms for these problems
proving the following results: - Isomorphism for bounded tree distance width
graphs is in L and thus complete for the class. We also show that for this kind
of graphs a canon can be computed within logspace. - For bounded treewidth
graphs, when both input graphs are given together with a tree decomposition,
the problem of whether there is an isomorphism which respects the
decompositions (i.e. considering only isomorphisms mapping bags in one
decomposition blockwise onto bags in the other decomposition) is in L. - For
bounded treewidth graphs, when one of the input graphs is given with a tree
decomposition the isomorphism problem is in LogCFL. - As a corollary the
isomorphism problem for bounded treewidth graphs is in LogCFL. This improves
the known TC1 upper bound for the problem given by Grohe and Verbitsky
[GroVer06].Comment: STACS conference 2010, 12 page
Reinterpreting deformations of the Heisenberg algebra
Minimal and maximal uncertainties of position measurements are widely
considered possible hallmarks of low-energy quantum as well as classical
gravity. While General Relativity describes interactions in terms of spatial
curvature, its quantum analogue may also extend to the realm of curved momentum
space as suggested, e. g. in the context of Relative Locality in Deformed
Special Relativity. Drawing on earlier work, we show in an entirely Born
reciprocal, i. e. position and momentum space covariant, way that the quadratic
Generalized Extended Uncertainty principle can alternatively be described in
terms of quantum dynamics on a general curved cotangent manifold. In the case
of the Extended Uncertainty Principle the curvature tensor in position space is
proportional to the noncommutativity of the momenta, while an analogous
relation applies to the curvature tensor in momentum space and the
noncommutativity of the coordinates for the Generalized Uncertainty Principle.
In the process of deriving this map, the covariance of the approach constrains
the admissible models to an interesting subclass of noncommutative geometries
which has not been studied before. Furthermore, we reverse the approach to
derive general anisotropically deformed uncertainty relations from general
background geometries. As an example, this formalism is applied to (anti)-de
Sitter spacetime.Comment: Error corrected, sections added, conclusions modified, 9 pages, no
figure
Precision measurement of the local bias of dark matter halos
We present accurate measurements of the linear, quadratic, and cubic local
bias of dark matter halos, using curved "separate universe" N-body simulations
which effectively incorporate an infinite-wavelength overdensity. This can be
seen as an exact implementation of the peak-background split argument. We
compare the results with the linear and quadratic bias measured from the
halo-matter power spectrum and bispectrum, and find good agreement. On the
other hand, the standard peak-background split applied to the Sheth & Tormen
(1999) and Tinker et al. (2008) halo mass functions matches the measured linear
bias parameter only at the level of 10%. The prediction from the excursion
set-peaks approach performs much better, which can be attributed to the
stochastic moving barrier employed in the excursion set-peaks prediction. We
also provide convenient fitting formulas for the nonlinear bias parameters
and , which work well over a range of redshifts.Comment: 23 pages, 8 figures; v2 : added references (sec. 1, 4, 5), results at
higher redshifts on fig. 4 and updated fitting formulas (eqs 5.2-5.3), v3 :
clarifications throughout, version accepted by JCA
Influence of defect-induced deformations on electron transport in carbon nanotubes
We theoretically investigate the influence of defect-induced long-range
deformations in carbon nanotubes on their electronic transport properties. To
this end we perform numerical ab-initio calculations using a
density-functional-based tight-binding (DFTB) model for various tubes with
vacancies. The geometry optimization leads to a change of the atomic positions.
There is a strong reconstruction of the atoms near the defect (called
"distortion") and there is an additional long-range deformation. The impact of
both structural features on the conductance is systematically investigated. We
compare short and long CNTs of different kinds with and without long-range
deformation. We find for the very thin (9,0)-CNT that the long-range
deformation additionally affects the transmission spectrum and the conductance
compared to the short-range lattice distortion. The conductance of the larger
(11,0)- or the (14,0)-CNT is overall less affected implying that the influence
of the long-range deformation decreases with increasing tube diameter.
Furthermore, the effect can be either positive or negative depending on the CNT
type and the defect type. Our results indicate that the long-range deformation
must be included in order to reliably describe the electronic structure of
defective, small-diameter zigzag tubes.Comment: Materials for Advanced Metallization 201
Separate Universe Simulations
The large-scale statistics of observables such as the galaxy density are
chiefly determined by their dependence on the local coarse-grained matter
density. This dependence can be measured directly and efficiently in N-body
simulations by using the fact that a uniform density perturbation with respect
to some fiducial background cosmology is equivalent to modifying the background
and including curvature, i.e., by simulating a "separate universe". We derive
this mapping to fully non-linear order, and provide a step-by-step description
of how to perform and analyse the separate universe simulations. This technique
can be applied to a wide range of observables. As an example, we calculate the
response of the non-linear matter power spectrum to long-wavelength density
perturbations, which corresponds to the angle-averaged squeezed limit of the
matter bispectrum and higher -point functions. Using only a modest
simulation volume, we obtain results with percent-level precision over a wide
range of scales.Comment: 5 pages, 2 figures, submitted to MNRAS. References added, typos
corrected. Added a paragraph on DE perturbation
The angle-averaged squeezed limit of nonlinear matter N-point functions
We show that in a certain, angle-averaged squeezed limit, the -point
function of matter is related to the response of the matter power spectrum to a
long-wavelength density perturbation,
, with . By performing
N-body simulations with a homogeneous overdensity superimposed on a flat
Friedmann-Robertson-Lema\^itre-Walker (FRLW) universe using the \emph{separate
universe} approach, we obtain measurements of the nonlinear matter power
spectrum response up to , which is equivalent to measuring the fully
nonlinear matter to point function in this squeezed limit. The
sub-percent to few percent accuracy of those measurements is unprecedented. We
then test the hypothesis that nonlinear -point functions at a given time are
a function of the linear power spectrum at that time, which is predicted by
standard perturbation theory (SPT) and its variants that are based on the ideal
pressureless fluid equations. Specifically, we compare the responses computed
from the separate universe simulations and simulations with a rescaled initial
(linear) power spectrum amplitude. We find discrepancies of 10\% at for to point functions at . The
discrepancy occurs at higher wavenumbers at . Thus, SPT and its variants,
carried out to arbitrarily high order, are guaranteed to fail to describe
matter -point functions () around that scale.Comment: 32 pages, 5 figures. Submitted to JCA
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