341 research outputs found

### 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

### 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

### 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

### 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

### 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 $n_\textrm{D}$ is given by $n_\textrm{D}
(n_\textrm{D} - 1)$; 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 $2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D})
[2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) - 1]$, in which $n_\textrm{C}$
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

### Effective Hamiltonian and unitarity of the S matrix

The properties of open quantum systems are described well by an effective
Hamiltonian ${\cal H}$ that consists of two parts: the Hamiltonian $H$ of the
closed system with discrete eigenstates and the coupling matrix $W$ between
discrete states and continuum. The eigenvalues of ${\cal H}$ determine the
poles of the $S$ matrix. The coupling matrix elements $\tilde W_k^{cc'}$
between the eigenstates $k$ of ${\cal H}$ and the continuum may be very
different from the coupling matrix elements $W_k^{cc'}$ between the eigenstates
of $H$ and the continuum. Due to the unitarity of the $S$ 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 $S$ matrix are given.Comment: 17 pages, 7 figure

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