336 research outputs found
R-matrix theory of driven electromagnetic cavities
Resonances of cylindrical symmetric microwave cavities are analyzed in
R-matrix theory which transforms the input channel conditions to the output
channels. Single and interfering double resonances are studied and compared
with experimental results, obtained with superconducting microwave cavities.
Because of the equivalence of the two-dimensional Helmholtz and the stationary
Schroedinger equations, the results present insight into the resonance
structure of regular and chaotic quantum billiards.Comment: Revtex 4.
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
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
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
First experimental evidence for quantum echoes in scattering systems
A self-pulsing effect termed quantum echoes has been observed in experiments
with an open superconducting and a normal conducting microwave billiard whose
geometry provides soft chaos, i.e. a mixed phase space portrait with a large
stable island. For such systems a periodic response to an incoming pulse has
been predicted. Its period has been associated to the degree of development of
a horseshoe describing the topology of the classical dynamics. The experiments
confirm this picture and reveal the topological information.Comment: RevTex 4.0, 5 eps-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
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
Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility
We propose an analysis technique for the exceptional points (EPs) occurring
in the discrete spectrum of open quantum systems (OQS), using a semi-infinite
chain coupled to an endpoint impurity as a prototype. We outline our method to
locate the EPs in OQS, further obtaining an eigenvalue expansion in the
vicinity of the EPs that gives rise to characteristic exponents. We also report
the precise number of EPs occurring in an OQS with a continuum described by a
quadratic dispersion curve. In particular, the number of EPs occurring in a
bare discrete Hamiltonian of dimension is given by ; if this discrete Hamiltonian is then coupled to continuum
(or continua) to form an OQS, the interaction with the continuum generally
produces an enlarged discrete solution space that includes a greater number of
EPs, specifically , in which
is the number of (non-degenerate) continua to which the discrete sector is
attached. Finally, we offer a heuristic quantum phase transition analogy for
the emergence of the resonance (giving rise to irreversibility via exponential
decay) in which the decay width plays the role of the order parameter; the
associated critical exponent is then determined by the above eigenvalue
expansion.Comment: 16 pages, 7 figure
Self-pulsing effect in chaotic scattering
We study the quantum and classical scattering of Hamiltonian systems whose
chaotic saddle is described by binary or ternary horseshoes. We are interested
in parameters of the system for which a stable island, associated with the
inner fundamental periodic orbit of the system exists and is large, but chaos
around this island is well developed. In this situation, in classical systems,
decay from the interaction region is algebraic, while in quantum systems it is
exponential due to tunneling. In both cases, the most surprising effect is a
periodic response to an incoming wave packet. The period of this self-pulsing
effect or scattering echoes coincides with the mean period, by which the
scattering trajectories rotate around the stable orbit. This period of rotation
is directly related to the development stage of the underlying horseshoe.
Therefore the predicted echoes will provide experimental access to topological
information. We numerically test these results in kicked one dimensional models
and in open billiards.Comment: Submitted to New Journal of Physics. Two movies (not included) and
full-resolution figures are available at http://www.cicc.unam.mx/~mejia
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
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