94 research outputs found
Semiclassical initial value calculations of collinear helium atom
Semiclassical calculations using the Herman-Kluk initial value treatment are
performed to determine energy eigenvalues of bound and resonance states of the
collinear helium atom. Both the configuration (where the classical motion
is fully chaotic) and the configuration (where the classical dynamics is
nearly integrable) are treated. The classical motion is regularized to remove
singularities that occur when the electrons collide with the nucleus. Very good
agreement is obtained with quantum energies for bound and resonance states
calculated by the complex rotation method.Comment: 24 pages, 3 figures. Submitted to J. Phys.
Alternative method to find orbits in chaotic systems
We present here a new method which applies well ordered symbolic dynamics to
find unstable periodic and non-periodic orbits in a chaotic system. The method
is simple and efficient and has been successfully applied to a number of
different systems such as the H\'enon map, disk billiards, stadium billiard,
wedge billiard, diamagnetic Kepler problem, colinear Helium atom and systems
with attracting potentials. The method seems to be better than earlier applied
methods.Comment: 5 pages, uuencoded compressed tar PostScript fil
Stability ordering of cycle expansions
We propose that cycle expansions be ordered with respect to stability rather
than orbit length for many chaotic systems, particularly those exhibiting
crises. This is illustrated with the strong field Lorentz gas, where we obtain
significant improvements over traditional approaches.Comment: Revtex, 5 incorporated figures, total size 200
The helium atom in a strong magnetic field
We investigate the electronic structure of the helium atom in a magnetic
field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic
system with two interactin g electrons and a fixed nucleus. Scaling laws are
provided connecting the fixed-nucleus Hamiltonia n to the one for the case of
finite nuclear mass. Respecting the symmetries of the electronic Ham iltonian
in the presence of a magnetic field, we represent this Hamiltonian as a matrix
with res pect to a two-particle basis composed of one-particle states of a
Gaussian basis set. The corresponding generalized eigenvalue problem is solved
numerically, providing in the present paper results for vanish ing magnetic
quantum number M=0 and even or odd z-parity, each for both singlet and triplet
spin symmetry. Total electronic energies of the ground state and the first few
excitations in each su bspace as well as their one-electron ionization energies
are presented as a function of the magnetic fie ld, and their behaviour is
discussed. Energy values for electromagnetic transitions within the M=0 sub
space are shown, and a complete table of wavelengths at all the detected
stationary points with respect to their field dependence is given, thereby
providing a basis for a comparison with observed ab sorption spectra of
magnetic white dwarfs.Comment: 21 pages, 4 Figures, acc.f.publ.in J.Phys.
Hydrogen atom moving across a strong magnetic field: analytical approximations
Analytical approximations are constructed for binding energies,
quantum-mechanical sizes and oscillator strengths of main radiative transitions
of hydrogen atoms arbitrarily moving in magnetic fields 10^{12}-10^{13} G.
Examples of using the obtained approximations for determination of maximum
transverse velocity of an atom and for evaluation of absorption spectra in
magnetic neutron star atmospheres are presented.Comment: 17 pages, 3 figures, 5 tables, LaTeX with IOP style files (included).
In v.2, Fig.1 and Table 5 have been corrected. In v.3, a misprint in the fit
for oscillator strengths, Eq.(21), has been correcte
Scars of Invariant Manifolds in Interacting Chaotic Few-Body Systems
We present a novel extension of the concept of scars for the wave functions
of classically chaotic few-body systems of identical particles with rotation
and permutation symmetry. Generically there exist manifolds in classical phase
space which are invariant under the action of a common subgroup of these two
symmetries. Such manifolds are associated with highly symmetric configurations.
If sufficiently stable, the quantum motion on such manifolds displays a notable
enhancement of the revival in the autocorrelation function which is not
directly associated with individual periodic orbits. Rather, it indicates some
degree of localization around an invariant manifold which has collective
characteristics that should be experimentally observable.Comment: 4 pages, RevTeX, 4 PS/EPS-figures, uses psfig.sty, quantum
computation changed, to be published in Physical Review Letter
Quantizing Constrained Systems: New Perspectives
We consider quantum mechanics on constrained surfaces which have
non-Euclidean metrics and variable Gaussian curvature. The old controversy
about the ambiguities involving terms in the Hamiltonian of order hbar^2
multiplying the Gaussian curvature is addressed. We set out to clarify the
matter by considering constraints to be the limits of large restoring forces as
the constraint coordinates deviate from their constrained values. We find
additional ambiguous terms of order hbar^2 involving freedom in the
constraining potentials, demonstrating that the classical constrained
Hamiltonian or Lagrangian cannot uniquely specify the quantization: the
ambiguity of directly quantizing a constrained system is inherently
unresolvable. However, there is never any problem with a physical quantum
system, which cannot have infinite constraint forces and always fluctuates
around the mean constraint values. The issue is addressed from the perspectives
of adiabatic approximations in quantum mechanics, Feynman path integrals, and
semiclassically in terms of adiabatic actions.Comment: 11 pages, 2 figure
A factorization of a super-conformal map
A super-conformal map and a minimal surface are factored into a product of
two maps by modeling the Euclidean four-space and the complex Euclidean plane
on the set of all quaternions. One of these two maps is a holomorphic map or a
meromorphic map. These conformal maps adopt properties of a holomorphic
function or a meromorphic function. Analogs of the Liouville theorem, the
Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem,
the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and
branch points of a super-conformal map are obtained.Comment: 21 page
Classical approach in quantum physics
The application of a classical approach to various quantum problems - the
secular perturbation approach to quantization of a hydrogen atom in external
fields and a helium atom, the adiabatic switching method for calculation of a
semiclassical spectrum of hydrogen atom in crossed electric and magnetic
fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's
approach to Stark problem, long-lived excited states of a helium atom recently
discovered with the help of Poincar section, inelastic
transitions in slow and fast electron-atom and ion-atom collisions - is
reviewed. Further, a classical representation in quantum theory is discussed.
In this representation the quantum states are treating as an ensemble of
classical states. This approach opens the way to an accurate description of the
initial and final states in classical trajectory Monte Carlo (CTMC) method and
a purely classical explanation of tunneling phenomenon. The general aspects of
the structure of the semiclassical series such as renormgroup symmetry,
criterion of accuracy and so on are reviewed as well. In conclusion, the
relation between quantum theory, classical physics and measurement is
discussed.Comment: This review paper was rejected from J.Phys.A with referee's comment
"The author has made many worthwhile contributions to semiclassical physics,
but this article does not meet the standard for a topical review"
Intermanifold similarities in partial photoionization cross sections of helium
Using the eigenchannel R-matrix method we calculate partial photoionization
cross sections from the ground state of the helium atom for incident photon
energies up to the N=9 manifold. The wide energy range covered by our
calculations permits a thorough investigation of general patterns in the cross
sections which were first discussed by Menzel and co-workers [Phys. Rev. A {\bf
54}, 2080 (1996)]. The existence of these patterns can easily be understood in
terms of propensity rules for autoionization. As the photon energy is increased
the regular patterns are locally interrupted by perturber states until they
fade out indicating the progressive break-down of the propensity rules and the
underlying approximate quantum numbers. We demonstrate that the destructive
influence of isolated perturbers can be compensated with an energy-dependent
quantum defect.Comment: 10 pages, 10 figures, replacement with some typos correcte
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