2 research outputs found
Scattering properties of a cut-circle billiard waveguide with two conical leads
We examine a two-dimensional electron waveguide with a cut-circle cavity and
conical leads. By considering Wigner delay times and the Landauer-B\"{u}ttiker
conductance for this system, we probe the effects of the closed billiard energy
spectrum on scattering properties in the limit of weakly coupled leads. We
investigate how lead placement and cavity shape affect these conductance and
time delay spectra of the waveguide.Comment: 18 pages, 11 figures, accepted for publication in Phys. Rev. E (Jan.
2001
Periodic orbit bifurcations and breakup of shearless invariant tori in nontwist systems
textThis thesis explores two nontwist systems: the spherical pendulum as an
example of a continuous one and the standard nontwist map (SNM) as an example
of a discrete one. Whereas the spherical pendulum is a concrete example of a physical
system exhibiting nontwist phenomena, the SNM is an abstract, numerically easily
accessible model permitting systematic studies of nontwist effects characteristic of a
wide range of applications.
For the spherical pendulum, a system that has captured physicists' and mathematicians'
interest for centuries, the gradual progress in understanding this seemingly
simple, but still not fully explored problem is outlined. The known solutions
for the unforced (integrable) spherical pendulum are reviewed and approximated by
power series. The approximations are then used to analytically calculate, for the
vertically forced case, xed points and low-period periodic orbits. These are found
to undergo collision phenomena typical for nontwist systems.
For the SNM, a detailed cartography of parameter space is developed, based
on periodic orbit collision curves and their branching thresholds, hyperbolic manifold
reconnection thresholds, and the boundary for the onset of global chaos. This is used
to nd meanders, multiple shearless curves, and extended scenarios for periodic orbit
reconnection/collision. Based on Greene's residue criterion, the breakup of new types
of shearless orbits: meanders, outer shearless tori, and a nonnoble torus is studied
in detail within the framework of renormalization theory.Physic