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