In this work, open microwave resonators have been investigated as a model system of a quantum dot.
Since quantum dots are micrometer-sized, measurements in quantum dots are still very difficult except for transport
measurement, but relatively simple in a microwave resonator. We fabricated a
flat resonator and a resonator with soft-wall potential
so that the shape corresponded to a quantum dot which has been investigated in the laboratory of J.P. Bird.
For a flat resonator, i.e. a resonator with a hard-wall
potential, periodically occurring scarred wave function families
are analyzed, and the associated orbits are identified. For
complicated wave function families, we use a Fourier spectroscopy.
Influence of an absorber center is investigated using Fourier
transform of transmission between the input and output leads. The
Fourier map is analyzed to identify scar families. The calculated
orbits lengths and the experimentally obtained values show very
By varying the height of the resonator, potentials can be
simulated, using the correspondence between quantum mechanics and
electrodynamics. Using this relation, a resonator with soft-wall
potential was fabricated. The shape of the potential corresponds
to the above mentioned quantum dot. The measured eigenfrequencies
for the periodic bouncing-ball scar families agree very well with
the theoretical values from a WKB approximation . The wave
function family of an X-like cross bouncing ball is used to obtain
evidence of dynamical tunneling. By phase difference analysis and
transport behavior, the presence of dynamical tunneling is proven.
In the last part of this work, the statistical properties of the
wave functions of an asymmetric open flat resonator are discussed.
Opening to the outside world of billiard makes the wave function
complex, since there is transport. This cross-over regime, from
real to imaginary of wave functions is investigated
opening of the billiard by frequency increasing. The phase
rigidity distribution which give the ratio between the real and
imaginary parts of the wave function, the long-range correlation
of intensity and the current density are compared with the
theoretical values calculated from the random
superposition of plane waves theory. For all
investigated quantities, a very good agreement between experiment
and theory is found.