217 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
Recommended from our members
EVALUATION OF WASTE PACKAGE EXTERNAL ENVIRONMENTAL CONDITION STUDY
The U. S. Department of Energy (DOE) is studying Yucca Mountain as the possible site for a permanent underground repository for disposal of spent nuclear fuel (SNF) and other high-level waste (HLW). The emplacement of high-level radioactive waste in Yucca Mountain will release a large amount of heat into the rock above and below the repository. Due to this heat, the rock temperature will rise, and then decrease when the production of decay heat falls below the rate at which heat escapes from the hot zone. In addition to raising the rock temperature, the heat will vaporize water, which will condense in cooler regions. The condensate water may drain back toward the emplacement drifts or it may ''shed'' through the pillars between emplacement drifts. Other effects, such as coupled chemical and mechanical processes, may influence the movement of water above, within, and below the emplacement drifts. This study examined near field environmental parameters that could have an effect on the waste package, including temperature, humidity, seepage rate, pH of seepage, chemistry (dissolved salts/minerals) of seepage, composition of drift atmosphere, colloids, and biota. This report is a Type I analysis performed in support of the development of System Description Documents (SDDs). A Type I analysis is a quantitative or qualitative analysis that may fulfill any of a variety of purposes associated with the Monitored Geologic Repository (MGR), other than providing direct analytical support for design output documents. A Type I analysis may establish design input, as defined in the ''Quality Assurance Requirements and Description'' (QARD) (DOE 1998). This study establishes a technical basis for emplacement drift (i.e. at the waste package surface) environment criteria to be considered in the development of the waste package design. The information will support development of several SDDs and resolve emplacement drift external environment questions in the criteria of those documents. This study supports the following System Description Documents (SDDs): Uncanistered SNF Disposal Container, Canistered SNF Disposal Container, DHLW Disposal Container, DOE Waste Forms Disposal Container, Non-Fuel Components Disposal Container, Naval SNF Disposal Container and Ex-Container Systems development. Minimum and maximum bounding values for the parameters described in the scope of this study are established to support environment criteria development for those systems
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
Effective Hamiltonian and unitarity of the S matrix
The properties of open quantum systems are described well by an effective
Hamiltonian that consists of two parts: the Hamiltonian of the
closed system with discrete eigenstates and the coupling matrix between
discrete states and continuum. The eigenvalues of determine the
poles of the matrix. The coupling matrix elements
between the eigenstates of and the continuum may be very
different from the coupling matrix elements between the eigenstates
of and the continuum. Due to the unitarity of the matrix, the
\TW_k^{cc'} depend on energy in a non-trivial manner, that conflicts with the
assumptions of some approaches to reactions in the overlapping regime. Explicit
expressions for the wave functions of the resonance states and for their phases
in the neighbourhood of, respectively, avoided level crossings in the complex
plane and double poles of the matrix are given.Comment: 17 pages, 7 figure
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
First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
We report on first experimental signatures for chaos-assisted tunneling in a
two-dimensional annular billiard. Measurements of microwave spectra from a
superconducting cavity with high frequency resolution are combined with
electromagnetic field distributions experimentally determined from a normal
conducting twin cavity with high spatial resolution to resolve eigenmodes with
properly identified quantum numbers. Distributions of so-called quasi-doublet
splittings serve as basic observables for the tunneling between whispering
gallery type modes localized to congruent, but distinct tori which are coupled
weakly to irregular eigenstates associated with the chaotic region in phase
space.Comment: 5 pages RevTex, 5 low-resolution figures (high-resolution figures:
http://linac.ikp.physik.tu-darmstadt.de/heiko/chaospub.html, to be published
in Phys. Rev. Let
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
Resonance-assisted tunneling in near-integrable systems
Dynamical tunneling between symmetry related invariant tori is studied in the
near-integrable regime. Using the kicked Harper model as an illustration, we
show that the exponential decay of the wave functions in the classically
forbidden region is modified due to coupling processes that are mediated by
classical resonances. This mechanism leads to a substantial deviation of the
splitting between quasi-degenerate eigenvalues from the purely exponential
decrease with 1 / hbar obtained for the integrable system. A simple
semiclassical framework, which takes into account the effect of the resonance
substructure on the KAM tori, allows to quantitatively reproduce the behavior
of the eigenvalue splittings.Comment: 4 pages, 2 figures, gzipped tar file, to appear in Phys. Rev. Lett,
text slightly condensed compared to first versio
- …