24,538 research outputs found
A non-hyponormal operator generating Stieltjes moment sequences
A linear operator in a complex Hilbert space \hh for which the set
\dzn{S} of its -vectors is dense in \hh and is a Stieltjes moment sequence for every f \in \dzn{S}
is said to generate Stieltjes moment sequences. It is shown that there exists a
closed non-hyponormal operator which generates Stieltjes moment sequences.
What is more, \dzn{S} is a core of any power of . This is
established with the help of a weighted shift on a directed tree with one
branching vertex. The main tool in the construction comes from the theory of
indeterminate Stieltjes moment sequences. As a consequence, it is shown that
there exists a non-hyponormal composition operator in an -space (over a
-finite measure space) which is injective, paranormal and which
generates Stieltjes moment sequences. In contrast to the case of abstract
Hilbert space operators, composition operators which are formally normal and
which generate Stieltjes moment sequences are always subnormal (in fact
normal). The independence assertion of Barry Simon's theorem which
parameterizes von Neumann extensions of a closed real symmetric operator with
deficiency indices is shown to be false
Suppression of Higgsino mediated proton decay by cancellations in GUTs and strings
A mechanism for the enhancement for proton lifetime in
supersymmetric/supergravity (SUSY/SUGRA) grand unified theories (GUTs) and in
string theory models is discussed where Higgsino mediated proton decay arising
from color triplets (anti-triplets) with charges and
is suppressed by an internal cancellation due to contributions
from different sources. We exhibit the mechanism for an SU(5) model with
Higgs multiplets in addition to the usual Higgs structure of
the minimal model. This model contains both and
Higgs color triplets (anti-triplets) and simple constraints allow for a
complete suppression of Higgsino mediated proton decay. Suppression of proton
decay in an SU(5) model with Planck scale contributions is also considered. The
suppression mechanism is then exhibited for an SO(10) model with a unified
Higgs structure involving representations.The SU(5)
decomposition of contains and
and the cancellation mechanism arises among these
contributions which mirrror the SU(5) case. The cancellation mechanism appears
to be more generally valid for a larger class of unification models.
Specifically the cancellation mechanism may play a role in string model
constructions to suppress proton decay from dimension five operators. The
mechanism allows for the suppression of proton decay consistent with current
data allowing for the possibility that proton decay may be visible in the next
round of nucleon stability experiment.Comment: 26 pages, no figures. Revtex 4. To appear in Physical Review
Anomalous microwave conductivity coherence peak in c-axis MgB2 thin film
The temperature dependence of the real part of the microwave complex
conductivity at 17.9 GHz obtained from surface impedance measurements of two
c-axis oriented MgB2 thin films reveals a pronounced maximum at a temperature
around 0.6 times the critical temperature. Calculations in the frame of a
two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that
this maximum corresponds to an anomalous coherence peak resembling the two-gap
nature of MgB2. Our model assumes there is no interband impurity scattering and
a weak interband pairing interaction, as suggested by bandstructure
calculations. In addition, the observation of a coherence peak indicates that
the pi-band is in the dirty limit and dominates the total conductivity of our
filmsComment: 10 pages, 4 figures, to be published in Phys. Rev. Let
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