4,795 research outputs found
Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem
The concept of measurement in classical scattering is interpreted as an
overlap of a particle packet with some area in phase space that describes the
detector. Considering that usually we record the passage of particles at some
point in space, a common detector is described e.g. for one-dimensional systems
as a narrow strip in phase space. We generalize this concept allowing this
strip to be transformed by some, possibly non-linear, canonical transformation,
introducing thus a canonically transformed detector. We show such detectors to
be useful in the context of the inverse scattering problem in situations where
recently discovered scattering echoes could not be seen without their help.
More relevant applications in quantum systems are suggested.Comment: 8 pages, 15 figures. Better figures can be found in the original
article, wich can be found in
http://www.sm.luth.se/~norbert/home_journal/electronic/v12s1.html Related
movies can be found in www.cicc.unam.mx/~mau
Symmetry breaking: A tool to unveil the topology of chaotic scattering with three degrees of freedom
We shall use symmetry breaking as a tool to attack the problem of identifying
the topology of chaotic scatteruing with more then two degrees of freedom.
specifically we discuss the structure of the homoclinic/heteroclinic tangle and
the connection between the chaotic invariant set, the scattering functions and
the singularities in the cross section for a class of scattering systems with
one open and two closed degrees of freedom.Comment: 13 pages and 8 figure
Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems
We derive Fourier's law for a completely coherent quasi one--dimensional
chaotic quantum system coupled locally to two heat baths at different
temperatures. We solve the master equation to first order in the temperature
difference. We show that the heat conductance can be expressed as a
thermodynamic equilibrium coefficient taken at some intermediate temperature.
We use that expression to show that for temperatures large compared to the mean
level spacing of the system, the heat conductance is inversely proportional to
the level density and, thus, inversely proportional to the length of the
system
Surprising relations between parametric level correlations and fidelity decay
Unexpected relations between fidelity decay and cross form--factor, i.e.,
parametric level correlations in the time domain are found both by a heuristic
argument and by comparing exact results, using supersymmetry techniques, in the
framework of random matrix theory. A power law decay near Heisenberg time, as a
function of the relevant parameter, is shown to be at the root of revivals
recently discovered for fidelity decay. For cross form--factors the revivals
are illustrated by a numerical study of a multiply kicked Ising spin chain.Comment: 4 pages 3 figure
Extraction of information about periodic orbits from scattering functions
As a contribution to the inverse scattering problem for classical chaotic
systems, we show that one can select sequences of intervals of continuity, each
of which yields the information about period, eigenvalue and symmetry of one
unstable periodic orbit.Comment: LaTeX, 13 pages (includes 5 eps-figures
Unified theory of bound and scattering molecular Rydberg states as quantum maps
Using a representation of multichannel quantum defect theory in terms of a
quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering
map to derive a generalized quantum map, that includes the continuum. We show,
that this representation not only simplifies the understanding of the method,
but moreover produces considerable numerical advantages. Finally we show under
what circumstances the usual semi-classical approximations yield satisfactory
results. In particular we see that singularities that cause problems in
semi-classics are irrelevant to the quantum map
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