17 research outputs found
Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
The famous question of Mark Kac "Can one hear the shape of a drum?"
addressing the unique connection between the shape of a planar region and the
spectrum of the corresponding Laplace operator can be legitimately extended to
scattering systems. In the modified version one asks whether the geometry of a
vibrating system can be determined by scattering experiments. We present the
first experimental approach to this problem in the case of microwave graphs
(networks) simulating quantum graphs. Our experimental results strongly
indicate a negative answer. To demonstrate this we consider scattering from a
pair of isospectral microwave networks consisting of vertices connected by
microwave coaxial cables and extended to scattering systems by connecting leads
to infinity to form isoscattering networks. We show that the amplitudes and
phases of the determinants of the scattering matrices of such networks are the
same within the experimental uncertainties. Furthermore, we demonstrate that
the scattering matrices of the networks are conjugated by the, so called,
transplantation relation.Comment: 3 figures; Physical Review Letters, 201
Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
We report on experimental studies of the distribution of the reflection
coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix
employing open microwave networks with symplectic symmetry and varying size of
absorption. The results are compared to analytical predictions derived for the
single-channel scattering case within the framework of random matrix theory
(RMT). Furthermore, we performed Monte Carlo simulations based on the
Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic
systems and the two-point correlation function of the S-matrix elements. The
analytical results and the Monte Carlo simulations depend on the size of
absorption. To verify them, we performed experiments with microwave networks
for various absorption strengths. We show that deviations from RMT predictions
observed in the spectral properties of the corresponding closed quantum graph,
and attributed to the presence of nonuniversal short periodic orbits, does not
have any visible effects on the distributions of the reflection coefficients
and the K and S matrices associated with the corresponding open quantum graph