Conductance fluctuations
Mesoscopic systems are systems which are neither microscopic nor macroscopic.
It is possible to observe quantum coherence effects in ``large'' systems.
An important class of models are ballistic quantum dots.
It is possible to build these such that
the resistance arises from elastic scattering of the
electrons with the sample and not because of impurities.
Depending on the classical dynamical properties inside
the quantum dot one gets different behaviour of
the conductance: For strongly chaotic samples
one gets universal conductance fluctuations
(as in diffusive systems).
However, for systems with mixed phase space the
chaotic dynamics is strongly influenced by islands.
The power law trapping on the classical side leads
to fractal conductance fluctuations, i.e. the
graph of the conductance vs. some parameter is a fractal.
In addition the graph of the conductance shows isolated peaks
in mixed systems. These isolated resonances and the resonant scattering
states can be associated to eigenstates of the closed system. They can
all be categorized as hierarchical or regular, depending on where the
corresponding eigenstates live in the classical phase space.
The figure shows the time delay as a function of the energy.
Resonances of the scattering system correspond to peaks which
can be associated with
eigenstates of the closed system. For a regular
and a hierarchical eigenstate the corresponding Husimi distributions
on the Poincaré section of the billiard are shown
(black corresponding to high intensity).
Reference:
Last modified: 27 October 2004, 16:21:50
Impressum, © Arnd Bäcker
