15,010 research outputs found
Eisenstein Series and String Thresholds
We investigate the relevance of Eisenstein series for representing certain
-invariant string theory amplitudes which receive corrections from BPS
states only. may stand for any of the mapping class, T-duality and
U-duality groups , or respectively.
Using -invariant mass formulae, we construct invariant modular functions
on the symmetric space of non-compact type, with the
maximal compact subgroup of , that generalize the standard
non-holomorphic Eisenstein series arising in harmonic analysis on the
fundamental domain of the Poincar\'e upper half-plane. Comparing the
asymptotics and eigenvalues of the Eisenstein series under second order
differential operators with quantities arising in one- and -loop string
amplitudes, we obtain a manifestly T-duality invariant representation of the
latter, conjecture their non-perturbative U-duality invariant extension, and
analyze the resulting non-perturbative effects. This includes the and
couplings in toroidal compactifications of M-theory to any
dimension and respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms
renumbered, plus minor corrections; v3: relation (1.7) to math Eis series
clarified, eq (3.3) and minor typos corrected, final version to appear in
Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde
General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL
We present a detailed implementation of two bispectrum estimation methods
which can be applied to general non-separable primordial and CMB bispectra. The
method exploits bispectrum mode decompositions on the domain of allowed
wavenumber or multipole values. Concrete mode examples constructed from
symmetrised tetrahedral polynomials are given, demonstrating rapid convergence
for known bispectra. We use these modes to generate simulated CMB maps of high
resolution (l > 2000) given an arbitrary primordial power spectrum and
bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum.
By extracting coefficients for the same separable basis functions from an
observational map, we are able to present an efficient and general f_NL
estimator for a given theoretical model. The estimator has two versions
comparing theoretical and observed coefficients at either primordial or late
times, thus encompassing a wider range of models, including secondary
anisotropies, lensing and cosmic strings. We provide examples and validation of
both f_NL estimation methods by direct comparison with simulations in a
WMAP-realistic context. In addition, we show how the full bispectrum can be
extracted from observational maps using these mode expansions, irrespective of
the theoretical model under study. We also propose a universal definition of
the bispectrum parameter F_NL for more consistent comparison between
theoretical models. We obtain WMAP5 estimates of f_NL for the equilateral model
from both our primordial and late-time estimators which are consistent with
each other, as well as with results already published in the literature. These
general bispectrum estimation methods should prove useful for the analysis of
nonGaussianity in the Planck satellite data, as well as in other contexts.Comment: 41 pages, 17 figure
Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase
We study the fidelity approach to quantum phase transitions (QPTs) and apply
it to general thermal phase transitions (PTs). We analyze two particular cases:
the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of
superconductivity. In both cases we show that the sudden drop of the mixed
state fidelity marks the line of the phase transition. We conduct a detailed
analysis of the general case of systems given by mutually commuting
Hamiltonians, where the non-analyticity of the fidelity is directly related to
the non-analyticity of the relevant response functions (susceptibility and heat
capacity), for the case of symmetry-breaking transitions. Further, on the case
of BCS theory of superconductivity, given by mutually non-commuting
Hamiltonians, we analyze the structure of the system's eigenvectors in the
vicinity of the line of the phase transition showing that their sudden change
is quantified by the emergence of a generically non-trivial Uhlmann mixed state
geometric phase.Comment: 18 pages, 8 figures. Version to be publishe
A computationally efficient method for calculating the maximum conductance of disordered networks: Application to 1-dimensional conductors
Random networks of carbon nanotubes and metallic nanowires have shown to be
very useful in the production of transparent, conducting films. The electronic
transport on the film depends considerably on the network properties, and on
the inter-wire coupling. Here we present a simple, computationally efficient
method for the calculation of conductance on random nanostructured networks.
The method is implemented on metallic nanowire networks, which are described
within a single-orbital tight binding Hamiltonian, and the conductance is
calculated with the Kubo formula. We show how the network conductance depends
on the average number of connections per wire, and on the number of wires
connected to the electrodes. We also show the effect of the inter-/intra-wire
hopping ratio on the conductance through the network. Furthermore, we argue
that this type of calculation is easily extendable to account for the upper
conductivity of realistic films spanned by tunneling networks. When compared to
experimental measurements, this quantity provides a clear indication of how
much room is available for improving the film conductivity.Comment: 7 pages, 5 figure
Towards absolute calibration of optical tweezers
Aiming at absolute force calibration of optical tweezers, following a
critical review of proposed theoretical models, we present and test the results
of MDSA (Mie-Debye-Spherical Aberration) theory, an extension of a previous
(MD) model, taking account of spherical aberration at the glass/water
interface. This first-principles theory is formulated entirely in terms of
experimentally accessible parameters (none adjustable). Careful experimental
tests of the MDSA theory, undertaken at two laboratories, with very different
setups, are described. A detailed description is given of the procedures
employed to measure laser beam waist, local beam power at the transparent
microspheres trapped by the tweezers, microsphere radius and the trap
transverse stiffness, as a function of radius and height in the (inverted
microscope) sample chamber. We find generally very good agreement with MDSA
theory predictions, for a wide size range, from the Rayleigh domain to large
radii, including the values most often employed in practice, and at different
chamber heights, both with objective overfilling and underfilling. The results
asymptotically approach geometrical optics in the mean over size intervals, as
they should, and this already happens for size parameters not much larger than
unity. MDSA predictions for the trapping threshold, position of stiffness peak,
stiffness variation with height, multiple equilibrium points and `hopping'
effects among them are verified. Remaining discrepancies are ascribed to focus
degradation, possibly arising from objective aberrations in the infrared, not
yet included in MDSA theory.Comment: 15 pages, 20 figure
Evaluation of RegCM4 over the CORDEX South America Domain: Sensitivity analysis to the Land Surface Scheme for the Amazon Basin.
Assessment of Climate change impacts on grain crops for the Southern Brazil projections from SA CORDEX.
k-deformed Poincare algebras and quantum Clifford-Hopf algebras
The Minkowski spacetime quantum Clifford algebra structure associated with
the conformal group and the Clifford-Hopf alternative k-deformed quantum
Poincare algebra is investigated in the Atiyah-Bott-Shapiro mod 8 theorem
context. The resulting algebra is equivalent to the deformed anti-de Sitter
algebra U_q(so(3,2)), when the associated Clifford-Hopf algebra is taken into
account, together with the associated quantum Clifford algebra and a (not
braided) deformation of the periodicity Atiyah-Bott-Shapiro theorem.Comment: 10 pages, RevTeX, one Section and references added, improved content
- âŠ