328 research outputs found
Phase shift experiments identifying Kramers doublets in a chaotic superconducting microwave billiard of threefold symmetry
The spectral properties of a two-dimensional microwave billiard showing
threefold symmetry have been studied with a new experimental technique. This
method is based on the behavior of the eigenmodes under variation of a phase
shift between two input channels, which strongly depends on the symmetries of
the eigenfunctions. Thereby a complete set of 108 Kramers doublets has been
identified by a simple and purely experimental method. This set clearly shows
Gaussian unitary ensemble statistics, although the system is time-reversal
invariant.Comment: RevTex 4, 5 figure
Experimental Test of a Trace Formula for a Chaotic Three Dimensional Microwave Cavity
We have measured resonance spectra in a superconducting microwave cavity with
the shape of a three-dimensional generalized Bunimovich stadium billiard and
analyzed their spectral fluctuation properties. The experimental length
spectrum exhibits contributions from periodic orbits of non-generic modes and
from unstable periodic orbit of the underlying classical system. It is well
reproduced by our theoretical calculations based on the trace formula derived
by Balian and Duplantier for chaotic electromagnetic cavities.Comment: 4 pages, 5 figures (reduced quality
Crossing of two Coulomb-Blockade Resonances
We investigate theoretically the transport of non--interacting electrons
through an Aharanov--Bohm (AB) interferometer with two quantum dots (QD)
embedded into its arms. In the Coulomb-blockade regime, transport through each
QD proceeds via a single resonance. The resonances are coupled through the arms
of the AB device but may also be coupled directly. In the framework of the
Landauer--Buttiker approach, we present expressions for the scattering matrix
which depend explicitly on the energies of the two resonances and on the AB
phase. We pay particular attention to the crossing of the two resonances.Comment: 15 pages, 1 figur
Adjacency Matrices of Configuration Graphs
In 1960, Hoffman and Singleton \cite{HS60} solved a celebrated equation for
square matrices of order , which can be written as where , , and are the identity matrix, the
all one matrix, and a --matrix with all row and column sums equal to
, respectively. If is an incidence matrix of some configuration
of type , then the left-hand side is an adjacency matrix of the non--collinearity
graph of . In certain situations, is also an
incidence matrix of some configuration, namely the neighbourhood
geometry of introduced by Lef\`evre-Percsy, Percsy, and Leemans
\cite{LPPL}.
The matrix operator can be reiterated and we pose the problem of
solving the generalised Hoffman--Singleton equation . In
particular, we classify all --matrices with all row and column sums
equal to , for , which are solutions of this equation. As
a by--product, we obtain characterisations for incidence matrices of the
configuration in Kantor's list \cite{Kantor} and the
configuration #1971 in Betten and Betten's list \cite{BB99}
Resonance scattering and singularities of the scattering function
Recent studies of transport phenomena with complex potentials are explained
by generic square root singularities of spectrum and eigenfunctions of
non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that
such singularities produce a significant effect upon the pole behaviour of the
scattering matrix, and more significantly upon the associated residues. This
mechanism explains why by proper choice of the system parameters the resonance
cross section is increased drastically in one channel and suppressed in the
other channel.Comment: 4 pages, 3 figure
Transition from Gaussian-orthogonal to Gaussian-unitary ensemble in a microwave billiard with threefold symmetry
Recently it has been shown that time-reversal invariant systems with discrete
symmetries may display in certain irreducible subspaces spectral statistics
corresponding to the Gaussian unitary ensemble (GUE) rather than to the
expected orthogonal one (GOE). A Kramers type degeneracy is predicted in such
situations. We present results for a microwave billiard with a threefold
rotational symmetry and with the option to display or break a reflection
symmetry. This allows us to observe the change from GOE to GUE statistics for
one subset of levels. Since it was not possible to separate the three
subspectra reliably, the number variances for the superimposed spectra were
studied. The experimental results are compared with a theoretical and numerical
study considering the effects of level splitting and level loss
Hjelmslev Geometry of Mutually Unbiased Bases
The basic combinatorial properties of a complete set of mutually unbiased
bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a
prime and r a positive integer, are shown to be qualitatively mimicked by the
configuration of points lying on a proper conic in a projective Hjelmslev plane
defined over a Galois ring of characteristic p^2 and rank r. The q vectors of a
basis of H\_q correspond to the q points of a (so-called) neighbour class and
the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour
classes on the conic.Comment: 4 pages, 1 figure; extended list of references, figure made more
illustrative and in colour; v3 - one more figure and section added, paper
made easier to follow, references update
Encircling an Exceptional Point
We calculate analytically the geometric phases that the eigenvectors of a
parametric dissipative two-state system described by a complex symmetric
Hamiltonian pick up when an exceptional point (EP) is encircled. An EP is a
parameter setting where the two eigenvalues and the corresponding eigenvectors
of the Hamiltonian coalesce. We show that it can be encircled on a path along
which the eigenvectors remain approximately real and discuss a microwave cavity
experiment, where such an encircling of an EP was realized. Since the
wavefunctions remain approximately real, they could be reconstructed from the
nodal lines of the recorded spatial intensity distributions of the electric
fields inside the resonator. We measured the geometric phases that occur when
an EP is encircled four times and thus confirmed that for our system an EP is a
branch point of fourth order.Comment: RevTex 4.0, four eps-figures (low resolution
Observation of a Chiral State in a Microwave Cavity
A microwave experiment has been realized to measure the phase difference of
the oscillating electric field at two points inside the cavity. The technique
has been applied to a dissipative resonator which exhibits a singularity --
called exceptional point -- in its eigenvalue and eigenvector spectrum. At the
singularity, two modes coalesce with a phase difference of We
conclude that the state excited at the singularity has a definitiv chirality.Comment: RevTex 4, 5 figure
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