6 research outputs found
Fictitious-time wave-packet dynamics in atomic systems
Gaussian wave packets (GWPs) are well suited as basis functions to describe
the time evolution of arbitrary wave functions in systems with nonsingular
smooth potentials. They are less so in atomic systems on account of the
singular behavior of the Coulomb potential. We present a time-dependent
variational method that makes the use of GWPs possible in the description of
propagation of quantum states also in these systems. We do so by a
regularization of the Coulomb potential, and by introduction of a fictitious
time coordinate in which the evolution of an initial state can be calculated
exactly and analytically for a pure Coulomb potential. Therefore in perturbed
atomic systems variational approximations only arise from those parts of the
potentials which deviate from the Coulomb potential. The method is applied to
the hydrogen atom in external magnetic and electric fields. It can be adapted
to systems with definite symmetries, and thus allows for a wide range of
applications.Comment: 11 pages, 2 figure
Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein
condensates with attractive 1/r interaction is investigated with both a
variational approach and numerically exact calculations. We show that these
condensates exhibit signatures known from the nonlinear dynamics of autonomous
Hamiltonian systems. The two stationary solutions created in a tangent
bifurcation at a critical value of the scattering length are identified as
elliptical and hyperbolical fixed points, corresponding to stable and unstable
stationary states of the condensate. The stable stationary state is surrounded
by elliptical islands, corresponding to condensates periodically oscillating in
time, whereas condensate wave functions in the unstable region undergo a
collapse within finite time. For negative scattering lengths below the tangent
bifurcation no stationary solutions exist, i.e., the condensate is always
unstable and collapses.Comment: Corrected the original usage of two inconsistent energy units in some
equations and in Figs. 2, 4, 5, and 6; 12 pages 12 figure
Bifurcations, order, and chaos in the Bose-Einstein condensation of dipolar gases
We apply a variational technique to solve the time-dependent Gross-Pitaevskii
equation for Bose-Einstein condensates in which an additional dipole-dipole
interaction between the atoms is present with the goal of modelling the
dynamics of such condensates. We show that universal stability thresholds for
the collapse of the condensates correspond to bifurcation points where always
two stationary solutions of the Gross-Pitaevskii equation disappear in a
tangent bifurcation, one dynamically stable and the other unstable. We point
out that the thresholds also correspond to "exceptional points," i.e. branching
singularities of the Hamiltonian. We analyse the dynamics of excited condensate
wave functions via Poincare surfaces of section for the condensate parameters
and find both regular and chaotic motion, corresponding to (quasi-)
periodically oscillating and irregularly fluctuating condensates, respectively.
Stable islands are found to persist up to energies well above the saddle point
of the mean-field energy, alongside with collapsing modes. The results are
applicable when the shape of the condensate is axisymmetric.Comment: 10 pages, 4 figures, minor changes in the text and additional
reference adde
Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits
With increasing energy the diamagnetic hydrogen atom undergoes a transition
from regular to chaotic classical dynamics, and the closed orbits pass through
various cascades of bifurcations. Closed orbit theory allows for the
semiclassical calculation of photoabsorption spectra of the diamagnetic
hydrogen atom. However, at the bifurcations the closed orbit contributions
diverge. The singularities can be removed with the help of uniform
semiclassical approximations which are constructed over a wide energy range for
different types of codimension one and two catastrophes. Using the uniform
approximations and applying the high-resolution harmonic inversion method we
calculate fully resolved semiclassical photoabsorption spectra, i.e.,
individual eigenenergies and transition matrix elements at laboratory magnetic
field strengths, and compare them with the results of exact quantum
calculations.Comment: 26 pages, 9 figures, submitted to J. Phys.
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: closed orbi