179 research outputs found
Torsional Alfven Waves in Solar Magnetic Flux Tubes of Axial Symmetry
Aims: Propagation and energy transfer of torsional Alfv\'en waves in solar
magnetic flux tubes of axial symmetry is studied. Methods: An analytical model
of a solar magnetic flux tube of axial symmetry is developed by specifying a
magnetic flux and deriving general analytical formulae for the equilibrium mass
density and a gas pressure. The main advantage of this model is that it can be
easily adopted to any axisymmetric magnetic structure. The model is used to
simulate numerically the propagation of nonlinear Alfv\'en waves in such 2D
flux tubes of axial symmetry embedded in the solar atmosphere. The waves are
excited by a localized pulse in the azimuthal component of velocity and
launched at the top of the solar photosphere, and they propagate through the
solar chromosphere, transition region, and into the solar corona. Results: The
results of our numerical simulations reveal a complex scenario of twisted
magnetic field lines and flows associated with torsional Alfv\'en waves as well
as energy transfer to the magnetoacoustic waves that are triggered by the
Alfv\'en waves and are akin to the vertical jet flows. Alfv\'en waves
experience about 5 % amplitude reflection at the transition region. Magnetic
(velocity) field perturbations experience attenuation (growth) with height is
agreement with analytical findings. Kinetic energy of magnetoacoustic waves
consists of 25 % of the total energy of Alfv\'en waves. The energy transfer may
lead to localized mass transport in the form of vertical jets, as well as to
localized heating as slow magnetoacoustic waves are prone to dissipation in the
inner corona.Comment: 12 pages; 12 Figures, Astron. Astrophys. (A&A); Comment :
High-resolution images will be appeared with the final pape
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
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
Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
Schroedinger equation H \psi=E \psi with PT - symmetric differential operator
H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on
L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at
a>0. The proof of this non-variational construction is given. Our Taylor series
form of \psi complements and completes the recent terminating solutions as
obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J.
Phys. A: Math. Gen., to appea
Hydrogen atom in crossed external fields reexemined by the moment method
Recurrence relations of perturbation theory for hydrogen ground state are
obtained. With their aid polarizabilities in constant perpendicular electric
and magnetic fields are computed up to 80th order. The high orders asymptotic
is compared with its quasiclassical estimate. For the case of arbitrary mutual
orientation of external fields a general sixth order formula is given.Comment: 11 pages, LaTeX, 2 figures (eps
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
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.
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
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