172 research outputs found
An equilibrium model for RFP plasmas in the presence of resonant tearing modes
The equilibrium of a finite-beta RFP plasma in the presence of
saturated-amplitude tearing modes is investigated. The singularities of the MHD
force balance equation JXB=grad(p) at the modes rational surfaces are resolved
through a proper regularization of the zeroth-order (equilibrium) profiles, by
setting to zero there the gradient of the pressure and parallel current
density. An equilibrium model, which satisfies the regularization rule at the
various rational surfaces, is developed. The comparison with the experimental
data from the Reversed Field eXperiment (RFX) gives encouraging results. The
model provides an easy tool for magnetic analysis: many aspects of the
perturbations can be analyzed and reconstructed.Comment: Final accepted version. 36 page
Ionization of hydrogen and hydrogenic ions by antiprotons
Presented here is a description of the ionization of hydrogen and hydrogenic
ions by antiproton-impact, based on very large scale numerical solutions of the
time-dependent Schr\"odinger equation in three spatial dimensions and on
analysis of the topology of the electronic eigenenergy surfaces in the plane of
complex internuclear distance. Comparison is made with other theories and very
recent measurements.Comment: RevTex document, 11 pages, 4 Postscript figures are available from
the authors, in press Phys. Rev. Let
Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross section shape
The equilibrium of a cylindrical plasma with purely poloidal mass flow and
cross section of arbitrary shape is investigated within the framework of the
ideal MHD theory. For the system under consideration it is shown that only
incompressible flows are possible and, conscequently, the general two
dimensional flow equilibrium equations reduce to a single second-order
quasilinear partial differential equation for the poloidal magnetic flux
function , in which four profile functionals of appear. Apart from
a singularity occuring when the modulus of Mach number associated with the
Alfv\'en velocity for the poloidal magnetic field is unity, this equation is
always elliptic and permits the construction of several classes of analytic
solutions. Specific exact equlibria for a plasma confined within a perfectly
conducting circular cylindrical boundary and having i) a flat current density
and ii) a peaked current density are obtained and studied.Comment: Accepted to Plasma Physics & Controlled Fusion, 14 pages, revte
Calculation of the properties of the rotational bands of Gd
We reexamine the long-standing problem of the microscopic derivation of a
particle-core coupling model. We base our research on the Klein-Kerman
approach, as amended by D\"onau and Frauendorf. We describe the formalism to
calculate energy spectra and transition strengths in some detail. We apply our
formalism to the rotational nuclei Gd, where recent experimental
data requires an explanation. We find no clear evidence of a need for Coriolis
attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st
Projective Hilbert space structures at exceptional points
A non-Hermitian complex symmetric 2x2 matrix toy model is used to study
projective Hilbert space structures in the vicinity of exceptional points
(EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are
Puiseux-expanded in terms of the root vectors at the EP. It is shown that the
apparent contradiction between the two incompatible normalization conditions
with finite and singular behavior in the EP-limit can be resolved by
projectively extending the original Hilbert space. The complementary
normalization conditions correspond then to two different affine charts of this
enlarged projective Hilbert space. Geometric phase and phase jump behavior are
analyzed and the usefulness of the phase rigidity as measure for the distance
to EP configurations is demonstrated. Finally, EP-related aspects of
PT-symmetrically extended Quantum Mechanics are discussed and a conjecture
concerning the quantum brachistochrone problem is formulated.Comment: 20 pages; discussion extended, refs added; bug correcte
Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge
We define the {\it rest-frame instant form} of tetrad gravity restricted to
Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of
gauge transformations generated by the 14 first class constraints of the
theory, we define and solve the multitemporal equations associated with the
rotation and space diffeomorphism constraints, finding how the cotriads and
their momenta depend on the corresponding gauge variables. This allows to find
quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal
gauges and to find the Dirac observables for superspace in these gauges.
The construction of the explicit form of the transformation and of the
solution of the rotation and supermomentum constraints is reduced to solve a
system of elliptic linear and quasi-linear partial differential equations. We
then show that the superhamiltonian constraint becomes the Lichnerowicz
equation for the conformal factor of the 3-metric and that the last gauge
variable is the momentum conjugated to the conformal factor. The gauge
transformations generated by the superhamiltonian constraint perform the
transitions among the allowed foliations of spacetime, so that the theory is
independent from its 3+1 splittings. In the special 3-orthogonal gauge defined
by the vanishing of the conformal factor momentum we determine the final Dirac
observables for the gravitational field even if we are not able to solve the
Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted
to this completely fixed gauge.Comment: RevTeX file, 141 page
From Heisenberg matrix mechanics to EBK quantization: theory and first applications
Despite the seminal connection between classical multiply-periodic motion and
Heisenberg matrix mechanics and the massive amount of work done on the
associated problem of semiclassical (EBK) quantization of bound states, we show
that there are, nevertheless, a number of previously unexploited aspects of
this relationship that bear on the quantum-classical correspondence. In
particular, we emphasize a quantum variational principle that implies the
classical variational principle for invariant tori. We also expose the more
indirect connection between commutation relations and quantization of action
variables. With the help of several standard models with one or two degrees of
freedom, we then illustrate how the methods of Heisenberg matrix mechanics
described in this paper may be used to obtain quantum solutions with a modest
increase in effort compared to semiclassical calculations. We also describe and
apply a method for obtaining leading quantum corrections to EBK results.
Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.
Adiabatic theory of Wannier threshold laws and ionization cross sections
The Wannier threshold law for three-particle fragmentation is reviewed. By integrating the Schroedinger equation along a path where the reaction coordinate R is complex, anharmonic corrections to the simple power law are obtained. These corrections are found to be non-analytic in the energy E, in contrast to the expected analytic dependence upon E
Elastic scattering of hadrons
Colliding high energy hadrons either produce new particles or scatter
elastically with their quantum numbers conserved and no other particles
produced. We consider the latter case here. Although inelastic processes
dominate at high energies, elastic scattering contributes considerably (18-25%)
to the total cross section. Its share first decreases and then increases at
higher energies. Small-angle scattering prevails at all energies. Some
characteristic features are seen that provide informationon the geometrical
structure of the colliding particles and the relevant dynamical mechanisms. The
steep Gaussian peak at small angles is followed by the exponential (Orear)
regime with some shoulders and dips, and then by a power-law drop.
Results from various theoretical approaches are compared with experimental
data. Phenomenological models claiming to describe this process are reviewed.
The unitarity condition predicts an exponential fall for the differential cross
section with an additional substructure to occur exactly between the low
momentum transfer diffraction cone and a power-law, hard parton scattering
regime under high momentum transfer. Data on the interference of the Coulomb
and nuclear parts of amplitudes at extremely small angles provide the value of
the real part of the forward scattering nuclear amplitude.
The real part of the elastic scattering amplitude and the contribution of
inelastic processes to the imaginary part of this amplitude (the so-called
overlap function) at nonforward transferred momenta are also discussed.
Problems related to the scaling behavior of the differential cross section are
considered. The power-law regime at highest momentum transfer is briefly
described.Comment: 72 pages, 11 Figures; modified Physics-Uspekhi 56 (2013)
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