168 research outputs found
Semiclassical quantization of the diamagnetic hydrogen atom with near action-degenerate periodic-orbit bunches
The existence of periodic orbit bunches is proven for the diamagnetic Kepler
problem. Members of each bunch are reconnected differently at self-encounters
in phase space but have nearly equal classical action and stability parameters.
Orbits can be grouped already on the level of the symbolic dynamics by
application of appropriate reconnection rules to the symbolic code in the
ternary alphabet. The periodic orbit bunches can significantly improve the
efficiency of semiclassical quantization methods for classically chaotic
systems, which suffer from the exponential proliferation of orbits. For the
diamagnetic hydrogen atom the use of one or few representatives of a periodic
orbit bunch in Gutzwiller's trace formula allows for the computation of
semiclassical spectra with a classical data set reduced by up to a factor of
20.Comment: 10 pages, 9 figure
Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates
We investigate a Bose-Einstein condensate with additional long-range dipolar
interaction in a cylindrically symmetric trap within a variational framework.
Compared to the ground state of this system, little attention has as yet been
payed to its unstable excited states. For thermal excitations, however, the
latter is of great interest, because it forms the "activated complex" that
mediates the collapse of the condensate. For a certain value of the s-wave
scatting length our investigations reveal a bifurcation in the transition
state, leading to the emergence of two additional and symmetry-breaking excited
states. Because these are of lower energy than their symmetric counterpart, we
predict the occurrence of a symmetry-breaking thermally induced collapse of
dipolar condensates. We show that its occurrence crucially depends on the trap
geometry and calculate the thermal decay rates of the system within leading
order transition state theory with the help of a uniform rate formula near the
rank-2 saddle which allows to smoothly pass the bifurcation.Comment: 6 pages, 3 figure
Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner
For systems whose classical dynamics is chaotic, it is generally believed
that the local statistical properties of the quantum energy levels are well
described by Random Matrix Theory. We present here two counterexamples - the
hydrogen atom in a magnetic field and the quartic oscillator - which display
nearest neighbor statistics strongly different from the usual Wigner
distribution. We interpret the results with a simple model using a set of
regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles
package, use csh to unpack (on Unix machine), to be published in Phys. Rev.
Let
Diffusion Monte Carlo calculations for the ground states of atoms and ions in neutron star magnetic fields
The diffusion quantum Monte Carlo method is extended to solve the old
theoretical physics problem of many-electron atoms and ions in intense magnetic
fields. The feature of our approach is the use of adiabatic approximation wave
functions augmented by a Jastrow factor as guiding functions to initialize the
quantum Monte Carlo prodecure. We calcula te the ground state energies of atoms
and ions with nuclear charges from Z= 2, 3, 4, ..., 26 for magnetic field
strengths relevant for neutron stars.Comment: 6 pages, 1 figure, proceedings of the "9th International Conference
on Path Integrals - New Trends and Perspectives", Max-Planck-Institut fur
Physik komplexer Systeme, Dresden, Germany, September 23 - 28, 2007, to be
published as a book by World Scientific, Singapore (2008
Classical, semiclassical, and quantum investigations of the 4-sphere scattering system
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering
system, is investigated with classical, semiclassical, and quantum mechanical
methods at various center-to-center separations of the spheres. The efficiency
and scaling properties of the computations are discussed by comparisons to the
two-dimensional 3-disk system. While in systems with few degrees of freedom
modern quantum calculations are, in general, numerically more efficient than
semiclassical methods, this situation can be reversed with increasing dimension
of the problem. For the 4-sphere system with large separations between the
spheres, we demonstrate the superiority of semiclassical versus quantum
calculations, i.e., semiclassical resonances can easily be obtained even in
energy regions which are unattainable with the currently available quantum
techniques. The 4-sphere system with touching spheres is a challenging problem
for both quantum and semiclassical techniques. Here, semiclassical resonances
are obtained via harmonic inversion of a cross-correlated periodic orbit
signal.Comment: 12 pages, 5 figures, submitted to Phys. Rev.
Statistics of Oscillator Strengths in Chaotic Systems
The statistical description of oscillator strengths for systems like hydrogen
in a magnetic field is developed by using the supermatrix nonlinear
-model. The correlator of oscillator strengths is found to have a
universal parametric and frequency dependence, and its analytical expression is
given. This universal expression applies to quantum chaotic systems with the
same generality as Wigner-Dyson statistics.Comment: 11 pages, REVTeX3+epsf, two EPS figures. Replaced by the published
version. Minor changes
Three Applications of the String-Inspired Technique to Quantum Electrodynamics
We discuss the following recent applications of the ``string-inspired''
worldline technique to calculations in quantum electrodynamics: i) Photon
splitting in a constant magnetic field, ii) The two-loop Euler-Heisenberg
Lagrangian, iii) A progress report on a recalculation of the three-loop QED
beta -- function.Comment: 10 pages, uuencoded Postscript-File, talk given by C. Schubert at the
Zeuthen Workshop on Elementary Particle Theory: QCD and QED in Higher Orders,
Rheinsberg, Germany, 21-26 Apr 199
Significance of Ghost Orbit Bifurcations in Semiclassical Spectra
Gutzwiller's trace formula for the semiclassical density of states in a
chaotic system diverges near bifurcations of periodic orbits, where it must be
replaced with uniform approximations. It is well known that, when applying
these approximations, complex predecessors of orbits created in the bifurcation
("ghost orbits") can produce pronounced signatures in the semiclassical spectra
in the vicinity of the bifurcation. It is the purpose of this paper to
demonstrate that these ghost orbits themselves can undergo bifurcations,
resulting in complex, nongeneric bifurcation scenarios. We do so by studying an
example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling
of the balloon orbit. By application of normal form theory we construct an
analytic description of the complete bifurcation scenario, which is then used
to calculate the pertinent uniform approximation. The ghost orbit bifurcation
turns out to produce signatures in the semiclassical spectrum in much the same
way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.
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