3,845 research outputs found
Factorization, Power Corrections, and the Pion Form Factor
This letter is an investigation of the pion form factor utilizing recently
developed effective field theory techniques. The primary results reported are:
Both the transition and electromagnetic form factors are corrected at order
. However, these corrections only arise due to time ordered products
which are sensitive to soft components of the pion. The usual higher twist wave
function corrections contribute only at order , when the quark
mass vanishes. In the case of the electromagnetic form factor the
power correction is enhanced by a power of relative to the
leading order result of Brodsky and Lepage, if the scale is
non-perturbative. This enhanced correction could explain the discrepancy with
the data.Comment: Published, extended, versio
Effective field theory approach to Casimir interactions on soft matter surfaces
We utilize an effective field theory approach to calculate Casimir
interactions between objects bound to thermally fluctuating fluid surfaces or
interfaces. This approach circumvents the complicated constraints imposed by
such objects on the functional integration measure by reverting to a point
particle representation. To capture the finite size effects, we perturb the
Hamiltonian by DH that encapsulates the particles' response to external fields.
DH is systematically expanded in a series of terms, each of which scales
homogeneously in the two power counting parameters: \lambda \equiv R/r, the
ratio of the typical object size (R) to the typical distance between them (r),
and delta=kB T/k, where k is the modulus characterizing the surface energy. The
coefficients of the terms in DH correspond to generalized polarizabilities and
thus the formalism applies to rigid as well as deformable objects.
Singularities induced by the point particle description can be dealt with using
standard renormalization techniques. We first illustrate and verify our
approach by re-deriving known pair forces between circular objects bound to
films or membranes. To demonstrate its efficiency and versatility, we then
derive a number of new results: The triplet interactions present in these
systems, a higher order correction to the film interaction, and general scaling
laws for the leading order interaction valid for objects of arbitrary shape and
internal flexibility.Comment: 4 pages, 1 figur
CMB Signals of Neutrino Mass Generation
We propose signals in the cosmic microwave background to probe the type and
spectrum of neutrino masses. In theories that have spontaneous breaking of
approximate lepton flavor symmetries at or below the weak scale, light
pseudo-Goldstone bosons recouple to the cosmic neutrinos after nucleosynthesis
and affect the acoustic oscillations of the electron-photon fluid during the eV
era. Deviations from the Standard Model are predicted for both the total energy
density in radiation during this epoch, \Delta N_nu, and for the multipole of
the n'th CMB peak at large n, \Delta l_n. The latter signal is difficult to
reproduce other than by scattering of the known neutrinos, and is therefore an
ideal test of our class of theories. In many models, the large shift, \Delta
l_n \approx 8 n_S, depends on the number of neutrino species that scatter via
the pseudo-Goldstone boson interaction. This interaction is proportional to the
neutrino masses, so that the signal reflects the neutrino spectrum. The
prediction for \Delta N_nu is highly model dependent, but can be accurately
computed within any given model. It is very sensitive to the number of
pseudo-Goldstone bosons, and therefore to the underlying symmetries of the
leptons, and is typically in the region of 0.03 < \Delta N_nu < 1. This signal
is significantly larger for Majorana neutrinos than for Dirac neutrinos, and,
like the scattering signal, varies as the spectrum of neutrinos is changed from
hierarchical to inverse hierarchical to degenerate.Comment: 40 pages, 4 figure
Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations
Using a one-dimensional macromolecule in aqueous solution as an illustration,
we demonstrate that the relative entropy from information theory, , has a natural role in the energetics of equilibrium and
nonequilibrium conformational fluctuations of the single molecule. It is
identified as the free energy difference associated with a fluctuating density
in equilibrium, and is associated with the distribution deviate from the
equilibrium in nonequilibrium relaxation. This result can be generalized to any
other isothermal macromolecular systems using the mathematical theories of
large deviations and Markov processes, and at the same time provides the
well-known mathematical results with an interesting physical interpretations.Comment: 5 page
Universality of Decoherence
We consider environment induced decoherence of quantum superpositions to
mixtures in the limit in which that process is much faster than any competing
one generated by the Hamiltonian of the isolated system. While
the golden rule then does not apply we can discard . By allowing
for simultaneous couplings to different reservoirs, we reveal decoherence as a
universal short-time phenomenon independent of the character of the system as
well as the bath and of the basis the superimposed states are taken from. We
discuss consequences for the classical behavior of the macroworld and quantum
measurement: For the decoherence of superpositions of macroscopically distinct
states the system Hamiltonian is always negligible.Comment: 4 revtex pages, no figure
The k-Point Random Matrix Kernels Obtained from One-Point Supermatrix Models
The k-point correlation functions of the Gaussian Random Matrix Ensembles are
certain determinants of functions which depend on only two arguments. They are
referred to as kernels, since they are the building blocks of all correlations.
We show that the kernels are obtained, for arbitrary level number, directly
from supermatrix models for one-point functions. More precisely, the generating
functions of the one-point functions are equivalent to the kernels. This is
surprising, because it implies that already the one-point generating function
holds essential information about the k-point correlations. This also
establishes a link to the averaged ratios of spectral determinants, i.e. of
characteristic polynomials
Finite size corrections to the radiation reaction force in classical electrodynamics
We introduce an effective field theory approach that describes the motion of
finite size objects under the influence of electromagnetic fields. We prove
that leading order effects due to the finite radius of a spherically
symmetric charge is order rather than order in any physical model, as
widely claimed in the literature. This scaling arises as a consequence of
Poincar\'e and gauge symmetries, which can be shown to exclude linear
corrections. We use the formalism to calculate the leading order finite size
correction to the Abraham-Lorentz-Dirac force.Comment: 4 pages, 2 figure
Canonical formulation of self-gravitating spinning-object systems
Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general
relativity, a canonical formulation of gravitationally interacting classical
spinning-object systems is given to linear order in spin. The constructed
position, linear momentum and spin variables fulfill standard Poisson bracket
relations. A spatially symmetric time gauge for the tetrad field is introduced.
The achieved formulation is of fully reduced form without unresolved
constraints, supplementary, gauge, or coordinate conditions. The canonical
field momentum is not related to the extrinsic curvature of spacelike
hypersurfaces in standard ADM form. A new reduction of the tetrad degrees of
freedom to the Einstein form of the metric field is suggested.Comment: 6 pages. v2: extended version; identical to the published one. v3:
corrected misprints in (24) and (39); improved notation; added note regarding
a further reference
Precision Measurements of Stretching and Compression in Fluid Mixing
The mixing of an impurity into a flowing fluid is an important process in
many areas of science, including geophysical processes, chemical reactors, and
microfluidic devices. In some cases, for example periodic flows, the concepts
of nonlinear dynamics provide a deep theoretical basis for understanding
mixing. Unfortunately, the building blocks of this theory, i.e. the fixed
points and invariant manifolds of the associated Poincare map, have remained
inaccessible to direct experimental study, thus limiting the insight that could
be obtained. Using precision measurements of tracer particle trajectories in a
two-dimensional fluid flow producing chaotic mixing, we directly measure the
time-dependent stretching and compression fields. These quantities, previously
available only numerically, attain local maxima along lines coinciding with the
stable and unstable manifolds, thus revealing the dynamical structures that
control mixing. Contours or level sets of a passive impurity field are found to
be aligned parallel to the lines of large compression (unstable manifolds) at
each instant. This connection appears to persist as the onset of turbulence is
approached.Comment: 5 pages, 5 figure
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