6 research outputs found
Crossover from Regular to Chaotic Behavior in the Conductance of Periodic Quantum Chains
The conductance of a waveguide containing finite number of periodically
placed identical point-like impurities is investigated. It has been calculated
as a function of both the impurity strength and the number of impurities using
the Landauer-B\"uttiker formula. In the case of few impurities the conductance
is proportional to the number of the open channels of the empty waveguide
and shows a regular staircase like behavior with step heights .
For large number of impurities the influence of the band structure of the
infinite periodic chain can be observed and the conductance is approximately
the number of energy bands (smaller than ) times the universal constant
. This lower value is reached exponentially with increasing number of
impurities. As the strength of the impurity is increased the system passes from
integrable to quantum-chaotic. The conductance, in units of , changes
from corresponding to the empty waveguide to corresponding to
chaotic or disordered system. It turnes out, that the conductance can be
expressed as where the parameter measures the chaoticity of
the system.Comment: 5 pages Revte
Diffraction in the semiclassical description of mesoscopic devices
In pseudo integrable systems diffractive scattering caused by wedges and
impurities can be described within the framework of Geometric Theory of
Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory
of Diffraction (POTD). We derive formulas expressing the reflection and
transition matrix elements for one and many diffractive points and apply it for
impurity and wedge diffraction. Diffraction can cause backscattering in
situations, where usual semiclassical backscattering is absent causing an
erodation of ideal conductance steps. The length of diffractive periodic orbits
and diffractive loops can be detected in the power spectrum of the reflection
matrix elements. The tail of the power spectrum shows decay
due to impurity scattering and decay due to wedge scattering.
We think this is a universal sign of the presence of diffractive scattering in
pseudo integrable waveguides.Comment: 18 pages, Latex , ep