15,948 research outputs found
Accurate determination of the Lagrangian bias for the dark matter halos
We use a new method, the cross power spectrum between the linear density
field and the halo number density field, to measure the Lagrangian bias for
dark matter halos. The method has several important advantages over the
conventional correlation function analysis. By applying this method to a set of
high-resolution simulations of 256^3 particles, we have accurately determined
the Lagrangian bias, over 4 magnitudes in halo mass, for four scale-free models
with the index n=-0.5, -1.0, -1.5 and -2.0 and three typical CDM models. Our
result for massive halos with ( is a characteristic non-linear
mass) is in very good agreement with the analytical formula of Mo & White for
the Lagrangian bias, but the analytical formula significantly underestimates
the Lagrangian clustering for the less massive halos $M < M_*. Our simulation
result however can be satisfactorily described, with an accuracy better than
15%, by the fitting formula of Jing for Eulerian bias under the assumption that
the Lagrangian clustering and the Eulerian clustering are related with a linear
mapping. It implies that it is the failure of the Press-Schechter theories for
describing the formation of small halos that leads to the inaccuracy of the Mo
& White formula for the Eulerian bias. The non-linear mapping between the
Lagrangian clustering and the Eulerian clustering, which was speculated as
another possible cause for the inaccuracy of the Mo & White formula, must at
most have a second-order effect. Our result indicates that the halo formation
model adopted by the Press-Schechter theories must be improved.Comment: Minor changes; accepted for publication in ApJ (Letters) ; 11 pages
with 2 figures include
Quantum Fully Homomorphic Encryption With Verification
Fully-homomorphic encryption (FHE) enables computation on encrypted data
while maintaining secrecy. Recent research has shown that such schemes exist
even for quantum computation. Given the numerous applications of classical FHE
(zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is
reasonable to hope that quantum FHE (or QFHE) will lead to many new results in
the quantum setting. However, a crucial ingredient in almost all applications
of FHE is circuit verification. Classically, verification is performed by
checking a transcript of the homomorphic computation. Quantumly, this strategy
is impossible due to no-cloning. This leads to an important open question: can
quantum computations be delegated and verified in a non-interactive manner? In
this work, we answer this question in the affirmative, by constructing a scheme
for QFHE with verification (vQFHE). Our scheme provides authenticated
encryption, and enables arbitrary polynomial-time quantum computations without
the need of interaction between client and server. Verification is almost
entirely classical; for computations that start and end with classical states,
it is completely classical. As a first application, we show how to construct
quantum one-time programs from classical one-time programs and vQFHE.Comment: 30 page
Warped Domain Wall Fermions
We consider Kaplan's domain wall fermions in the presence of an Anti-de
Sitter (AdS) background in the extra dimension. Just as in the flat space case,
in a completely vector-like gauge theory defined after discretizing this extra
dimension, the spectrum contains a very light charged fermion whose chiral
components are localized at the ends of the extra dimensional interval. The
component on the IR boundary of the AdS space can be given a large mass by
coupling it to a neutral fermion via the Higgs mechanism. In this theory, gauge
invariance can be restored either by taking the limit of infinite proper length
of the extra dimension or by reducing the AdS curvature radius towards zero. In
the latter case, the Kaluza-Klein modes stay heavy and the resulting classical
theory approaches a chiral gauge theory, as we verify numerically. Potential
difficulties for this approach could arise from the coupling of the
longitudinal mode of the light gauge boson, which has to be treated
non-perturbatively
Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields
We study the arithmetic of Eisenstein cohomology classes (in the sense of G.
Harder) for symmetric spaces associated to GL_2 over imaginary quadratic
fields. We prove in many cases a lower bound on their denominator in terms of a
special L-value of a Hecke character providing evidence for a conjecture of
Harder that the denominator is given by this L-value. We also prove under some
additional assumptions that the restriction of the classes to the boundary of
the Borel-Serre compactification of the spaces is integral. Such classes are
interesting for their use in congruences with cuspidal classes to prove
connections between the special L-value and the size of the Selmer group of the
Hecke character.Comment: 37 pages; strengthened integrality result (Proposition 16), corrected
statement of Theorem 3, and revised introductio
Cauchy's infinitesimals, his sum theorem, and foundational paradigms
Cauchy's sum theorem is a prototype of what is today a basic result on the
convergence of a series of functions in undergraduate analysis. We seek to
interpret Cauchy's proof, and discuss the related epistemological questions
involved in comparing distinct interpretive paradigms. Cauchy's proof is often
interpreted in the modern framework of a Weierstrassian paradigm. We analyze
Cauchy's proof closely and show that it finds closer proxies in a different
modern framework.
Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation;
uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc
A Simple Explanation for DAMA with Moderate Channeling
We consider the possibility that the DAMA signal arises from channeled events
in simple models where the dark matter interaction with nuclei is suppressed at
small momenta. As with the standard WIMP, these models have two parameters (the
dark matter mass and the size of the cross-section), without the need to
introduce an additional energy threshold type of parameter. We find that they
can be consistent with channeling fractions as low as about ~ 15%, so long as
at least ~70% of the nuclear recoil energy for channeled events is deposited
electronically. Given that there are reasons not to expect very large
channeling fractions, these scenarios make the channeling explanation of DAMA
much more compelling.Comment: 6 pages, 2 figure
Detailed analysis of the gluonic excitation in the three-quark system in lattice QCD
We study the excited-state potential and the gluonic excitation in the static
three-quark (3Q) system using SU(3) lattice QCD with at
=5.8 and 6.0 at the quenched level. For about 100 different patterns of
spatially-fixed 3Q systems, we accurately extract the excited-state potential
together with the ground-state potential by diagonalizing the QCD Hamiltonian in the presence of three
quarks. The gluonic excitation energy is found to be about 1 GeV at the typical hadronic
scale. This large gluonic-excitation energy is conjectured to give a physical
reason of the success of the quark model for low-lying hadrons even without
explicit gluonic modes. We investigate the functional form of in terms of the 3Q location. The lattice data of are
relatively well reproduced by the ``inverse Mercedes Ansatz'' with the
``modified Y-type flux-tube length'', which indicates that the
gluonic-excitation mode is realized as a complicated bulk excitation of the
whole 3Q system.Comment: 13pages, 13figure
Conserved Charges in Einstein Gauss-Bonnet theory
Using Noether's identities, we define a superpotential with respect to a
background for the Einstein Gauss-Bonnet theory of gravity. As an example, we
show that its associated conserved charge yields the mass-energy of a
D-dimensional Gauss-Bonnet black hole in an anti-de Sitter spacetime.Comment: 17 pages, LaTeX, references added, typos corrected, version to appear
in Class. Quant. Gra
Metallic behaviour of carrier-polarized C molecular layers: Experiment and Theory
Although C is a molecular crystal with a bandgap E of ~2.5 eV, we
show that E is strongly affected by injected charge. In sharp contrast to
the Coulomb blockade typical of quantum dots, E is {\it reduced} by the
Coulomb effects. The conductance of a thin C layer sandwiched between
metal (Al, Ag, Au, Mg and Pt) contacts is investigated. Excellent Ohmic
conductance is observed for Al electrodes protected with ultra-thin LiF layers.
First-principles calculations, Hubbard models etc., show that the energy gap of
C is dramatically reduced when electrons hop from C to
C.Comment: 4 PRL style pages, 2 figures. email: [email protected]
The Halo Mass Function: High-Redshift Evolution and Universality
We study the formation of dark matter halos in the concordance LCDM model
over a wide range of redshifts, from z=20 to the present. Our primary focus is
the halo mass function, a key probe of cosmology. By performing a large suite
of nested-box N-body simulations with careful convergence and error controls
(60 simulations with box sizes from 4 to 256 Mpc/h, we determine the mass
function and its evolution with excellent statistical and systematic errors,
reaching a few percent over most of the considered redshift and mass range.
Across the studied redshifts, the halo mass is probed over 6 orders of
magnitude (10^7 - 10^13.5 M_sun/h). Historically, there has been considerable
variation in the high redshift mass function as obtained by different groups.
We have made a concerted effort to identify and correct possible systematic
errors in computing the mass function at high redshift and to explain the
discrepancies between some of the previous results. We discuss convergence
criteria for the required force resolution, simulation box size, halo mass
range, initial and final redshift, and time stepping. Because of conservative
cuts on the mass range probed by individual boxes, our results are relatively
insensitive to simulation volume, the remaining sensitivity being consistent
with extended Press-Schechter theory. Previously obtained mass function fits
near z=0, when scaled by linear theory, are in good agreement with our results
at all redshifts, although a mild redshift dependence consistent with that
found by Reed and collaborators exists at low redshifts.Comment: 20 pages, 15 figures. Minor changes to the text and figures; results
and conclusions unchange
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