40,214 research outputs found
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
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
Quantum and classical echoes in scattering systems described by simple Smale horseshoes
We explore the quantum scattering of systems classically described by binary
and other low order Smale horseshoes, in a stage of development where the
stable island associated with the inner periodic orbit is large, but chaos
around this island is well developed. For short incoming pulses we find
periodic echoes modulating an exponential decay over many periods. The period
is directly related to the development stage of the horseshoe. We exemplify our
studies with a one-dimensional system periodically kicked in time and we
mention possible experiments.Comment: 7 pages with 6 reduced quality figures! Please contact the authors
([email protected]) for an original good quality pre-prin
Magneto-electric coupling in zigzag graphene nanoribbons
Zigzag graphene nanoribbons can have magnetic ground states with
ferromagnetic, antiferromagnetic, or canted configurations, depending on
carrier density. We show that an electric field directed across the ribbon
alters the magnetic state, favoring antiferromagnetic configurations. This
property can be used to prepare ribbons with a prescribed spin-orientation on a
given edge.Comment: 4 pages, 5 figure
Measurements of a Quantum Dot with an Impedance-Matching On-Chip LC Resonator at GHz Frequencies
We report the realization of a bonded-bridge on-chip superconducting coil and
its use in impedance-matching a highly ohmic quantum dot (QD) to a
measurement setup. The coil, modeled as a lumped-element resonator, is
more compact and has a wider bandwidth than resonators based on coplanar
transmission lines (e.g. impedance transformers and stub tuners) at
potentially better signal-to-noise ratios. In particular for measurements of
radiation emitted by the device, such as shot noise, the 50 larger
bandwidth reduces the time to acquire the spectral density. The resonance
frequency, close to 3.25 GHz, is three times higher than that of the one
previously reported wire-bonded coil. As a proof of principle, we fabricated an
circuit that achieves impedance-matching to a load
and validate it with a load defined by a carbon nanotube QD of which we measure
the shot noise in the Coulomb blockade regime.Comment: 7 pages, 6 figure
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
Shot noise of a quantum dot measured with GHz stub impedance matching
The demand for a fast high-frequency read-out of high impedance devices, such
as quantum dots, necessitates impedance matching. Here we use a resonant
impedance matching circuit (a stub tuner) realized by on-chip superconducting
transmission lines to measure the electronic shot noise of a carbon nanotube
quantum dot at a frequency close to 3 GHz in an efficient way. As compared to
wide-band detection without impedance matching, the signal to noise ratio can
be enhanced by as much as a factor of 800 for a device with an impedance of 100
k. The advantage of the stub resonator concept is the ease with which
the response of the circuit can be predicted, designed and fabricated. We
further demonstrate that all relevant matching circuit parameters can reliably
be deduced from power reflectance measurements and then used to predict the
power transmission function from the device through the circuit. The shot noise
of the carbon nanotube quantum dot in the Coulomb blockade regime shows an
oscillating suppression below the Schottky value of , as well an
enhancement in specific regions.Comment: 6 pages, 4 figures, supplementar
Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set
We study the classical electron scattering from a driven inverted Gaussian
potential, an open system, in terms of its chaotic invariant set. This chaotic
invariant set is described by a ternary horseshoe construction on an
appropriate Poincare surface of section. We find the development parameters
that describe the hyperbolic component of the chaotic invariant set. In
addition, we show that the hierarchical structure of the fractal set of
singularities of the scattering functions is the same as the structure of the
chaotic invariant set. Finally, we construct a symbolic encoding of the
hierarchical structure of the set of singularities of the scattering functions
and use concepts from the thermodynamical formalism to obtain one of the
measures of chaos of the fractal set of singularities, the topological entropy.Comment: accepted in Phy. Rev.
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