4,122 research outputs found
A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition
The Gutzwiller semiclassical trace formula links the eigenvalues of the
Scrodinger operator ^H with the closed orbits of the corresponding classical
mechanical system, associated with the Hamiltonian H, when the Planck constant
is small ("semiclassical regime"). Gutzwiller gave a heuristic proof, using the
Feynman integral representation for the propagator of ^H. Later on
mathematicians gave rigorous proofs of this trace formula, under different
settings, using the theory of Fourier Integral Operators and Lagrangian
manifolds. Here we want to show how the use of coherent states (or gaussian
beams) allows us to give a simple and direct proof.Comment: 17 pages, LaTeX, available on http://qcd.th.u-psud.f
The Relative Lie Algebra Cohomology of the Weil Representation of SO(n,1)
In Part 1 of this paper we construct a spectral sequence converging to the
relative Lie algebra cohomology associated to the action of any subgroup of
the symplectic group on the polynomial Fock model of the Weil representation,
see Section 7. These relative Lie algebra cohomology groups are of interest
because they map to the cohomology of suitable arithmetic quotients of the
symmetric space of . We apply this spectral sequence to the case in Sections 8, 9, and 10 to compute the relative Lie
algebra cohomology groups . Here is Minkowski space and
is the subspace of consisting of all products of
polynomials with the Gaussian. In Part 2 of this paper we compute the
cohomology groups using spectral theory and representation theory. In Part 3 of this paper
we compute the maps between the polynomial Fock and cohomology groups
induced by the inclusions .Comment: 64 pages, 5 figure
Hadron Helicity Violation in Exclusive Processes: Quantitative Calculations in Leading Order QCD
We study a new mechanism for hadronic helicity flip in high energy hard
exclusive reactions. The mechanism proceeds in the limit of perfect chiral
symmetry, namely without any need to flip a quark helicity. The fundamental
feature of the new mechanism is the breaking of rotational symmetry of the hard
collision by a scattering plane in processes involving independent quark
scattering. We show that in the impulse approximation there is no evidence for
of the helicity violating process as the energy or momentum transfer is
increased over the region 1 GeV^2 < Q^2 < 100 GeV^2. In the asymptotic region
Q^2> 1000 GeV^2, a saddle point approximation with doubly logarithmic accuracy
yields suppression by a fraction of power of Q^2. ``Chirally--odd" exclusive
wave functions which carry non--zero orbital angular momentum and yet are
leading order in the high energy limit, play an important role.Comment: uuencoded LaTeX file (21 pages) and PostScript figure
Covariant Symmetry Classifications for Observables of Cosmological Birefringence
Polarizations of electromagnetic waves from distant galaxies are known to be
correlated with the source orientations. These quantities have been used to
search for signals of cosmological birefringence. We review and classify
transformation properties of the polarization and source orientation
observables. The classifications give a firm foundation to certain practices
which have sprung up informally in the literature. Transformations under parity
play a central role, showing that parity violation in emission or in the
subsequent propagation is an observable phenomenon. We also discuss statistical
measures, correlations and distributions which transform properly and which can
be used for systematic data analysis.Comment: 8 pages, revtex, 1 postscript figur
The Virgo Alignment Puzzle in Propagation of Radiation on Cosmological Scales
We reconsider analysis of data on the cosmic microwave background on the
largest angular scales. Temperature multipoles of any order factor naturally
into a direct product of axial quantities and cosets. Striking coincidences
exist among the axes associated with the dipole, quadrupole, and octupole CMB
moments. These axes also coincide well with two other axes independently
determined from polarizations at radio and optical frequencies propagating on
cosmological scales. The five coincident axes indicate physical correlation and
anisotropic properties of the cosmic medium not predicted by the conventional
Big Bang scenario. We consider various mechanisms, including foreground
corrections, as candidates for the observed correlations. We also consider
whether the propagation anomalies may be a signal of ``dark energy'' in the
form of a condensed background field. Perhaps {\it light propagation} will
prove to be an effective way to look for the effects of {\it dark energy}.Comment: 24 pages, 4 figures, minor changes, no change in result or
conclusions. to appear in IJMP
Quantum tomography for collider physics: Illustrations with lepton pair production
Quantum tomography is a method to experimentally extract all that is
observable about a quantum mechanical system. We introduce quantum tomography
to collider physics with the illustration of the angular distribution of lepton
pairs. The tomographic method bypasses much of the field-theoretic formalism to
concentrate on what can be observed with experimental data, and how to
characterize the data. We provide a practical, experimentally-driven guide to
model-independent analysis using density matrices at every step. Comparison
with traditional methods of analyzing angular correlations of inclusive
reactions finds many advantages in the tomographic method, which include
manifest Lorentz covariance, direct incorporation of positivity constraints,
exhaustively complete polarization information, and new invariants free from
frame conventions. For example, experimental data can determine the
of the production process, which is a
model-independent invariant that measures the degree of coherence of the
subprocess. We give reproducible numerical examples and provide a supplemental
standalone computer code that implements the procedure. We also highlight a
property of that guarantees in a least-squares type fit
that a local minimum of a statistic will be a global minimum: There
are no isolated local minima. This property with an automated implementation of
positivity promises to mitigate issues relating to multiple minima and
convention-dependence that have been problematic in previous work on angular
distributions.Comment: 25 pages, 3 figure
IDENTIFYING PRIORITIES FOR PESTICIDE RESIDUE REDUCTION
Pesticide residues, dietary intakes, dietary risks, fruits and vegetables, Crop Production/Industries,
Knudsen gas provides nanobubble stability
We provide a model for the remarkable stability of surface nanobubbles to
bulk dissolution. The key to the solution is that the gas in a nanobubble is of
Knudsen type. This leads to the generation of a bulk liquid flow which
effectively forces the diffusive gas to remain local. Our model predicts the
presence of a vertical water jet immediately above a nanobubble, with an
estimated speed of , in good agreement with our
experimental atomic force microscopy measurement of . In
addition, our model also predicts an upper bound for the size of nanobubbles,
which is consistent with the available experimental data
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