1,964 research outputs found
On statistically stationary homogeneous shear turbulence
A statistically stationary turbulence with a mean shear gradient is realized
in a flow driven by suitable body forces. The flow domain is periodic in
downstream and spanwise directions and bounded by stress free surfaces in the
normal direction. Except for small layers near the surfaces the flow is
homogeneous. The fluctuations in turbulent energy are less violent than in the
simulations using remeshing, but the anisotropy on small scales as measured by
the skewness of derivatives is similar and decays weakly with increasing
Reynolds number.Comment: 4 pages, 5 figures (Figs. 3 and 4 as external JPG-Files
Shear-flow transition: the basin boundary
The structure of the basin of attraction of a stable equilibrium point is
investigated for a dynamical system (W97) often used to model transition to
turbulence in shear flows. The basin boundary contains not only an equilibrium
point Xlb but also a periodic orbit P, and it is the latter that mediates the
transition. Orbits starting near Xlb relaminarize. We offer evidence that this
is due to the extreme narrowness of the region complementary to basin of
attraction in that part of phase space near Xlb. This leads to a proposal for
interpreting the 'edge of chaos' in terms of more familiar invariant sets.Comment: 11 pages; submitted for publication in Nonlinearit
Symmetry Decomposition of Chaotic Dynamics
Discrete symmetries of dynamical flows give rise to relations between
periodic orbits, reduce the dynamics to a fundamental domain, and lead to
factorizations of zeta functions. These factorizations in turn reduce the labor
and improve the convergence of cycle expansions for classical and quantum
spectra associated with the flow. In this paper the general formalism is
developed, with the -disk pinball model used as a concrete example and a
series of physically interesting cases worked out in detail.Comment: CYCLER Paper 93mar01
Semiclassical cross section correlations
We calculate within a semiclassical approximation the autocorrelation
function of cross sections. The starting point is the semiclassical expression
for the diagonal matrix elements of an operator. For general operators with a
smooth classical limit the autocorrelation function of such matrix elements has
two contributions with relative weights determined by classical dynamics. We
show how the random matrix result can be obtained if the operator approaches a
projector onto a single initial state. The expressions are verified in
calculations for the kicked rotor.Comment: 6 pages, 2 figure
Approach to ergodicity in quantum wave functions
According to theorems of Shnirelman and followers, in the semiclassical limit
the quantum wavefunctions of classically ergodic systems tend to the
microcanonical density on the energy shell. We here develop a semiclassical
theory that relates the rate of approach to the decay of certain classical
fluctuations. For uniformly hyperbolic systems we find that the variance of the
quantum matrix elements is proportional to the variance of the integral of the
associated classical operator over trajectory segments of length , and
inversely proportional to , where is the Heisenberg
time, being the mean density of states. Since for these systems the
classical variance increases linearly with , the variance of the matrix
elements decays like . For non-hyperbolic systems, like Hamiltonians
with a mixed phase space and the stadium billiard, our results predict a slower
decay due to sticking in marginally unstable regions. Numerical computations
supporting these conclusions are presented for the bakers map and the hydrogen
atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and
uuencoded using uufiles, to appear in Phys Rev E. For related papers, see
http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm
Chaos and Correspondence in Classical and Quantum Hamiltonian Ratchets: A Heisenberg Approach
Previous work [Gong and Brumer, Phys. Rev. Lett., 97, 240602 (2006)]
motivates this study as to how asymmetry-driven quantum ratchet effects can
persist despite a corresponding fully chaotic classical phase space. A simple
perspective of ratchet dynamics, based on the Heisenberg picture, is
introduced. We show that ratchet effects are in principle of common origin in
classical and quantum mechanics, though full chaos suppresses these effects in
the former but not necessarily the latter. The relationship between ratchet
effects and coherent dynamical control is noted.Comment: 21 pages, 7 figures, to appear in Phys. Rev.
Small Disks and Semiclassical Resonances
We study the effect on quantum spectra of the existence of small circular
disks in a billiard system. In the limit where the disk radii vanish there is
no effect, however this limit is approached very slowly so that even very small
radii have comparatively large effects. We include diffractive orbits which
scatter off the small disks in the periodic orbit expansion. This situation is
formally similar to edge diffraction except that the disk radii introduce a
length scale in the problem such that for wave lengths smaller than the order
of the disk radius we recover the usual semi-classical approximation; however,
for wave lengths larger than the order of the disk radius there is a
qualitatively different behaviour. We test the theory by successfully
estimating the positions of scattering resonances in geometries consisting of
three and four small disks.Comment: Final published version - some changes in the discussion and the
labels on one figure are correcte
Non-sequential triple ionization in strong fields
We consider the final stage of triple ionization of atoms in a strong
linearly polarized laser field. We propose that for intensities below the
saturation value for triple ionization the process is dominated by the
simultaneous escape of three electrons from a highly excited intermediate
complex. We identify within a classical model two pathways to triple
ionization, one with a triangular configuration of electrons and one with a
more linear one. Both are saddles in phase space. A stability analysis
indicates that the triangular configuration has the larger cross sections and
should be the dominant one. Trajectory simulations within the dominant symmetry
subspace reproduce the experimentally observed distribution of ion momenta
parallel to the polarization axis.Comment: 9 pages, 8 figures, accepted for publication in Phys. Rev.
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