18,166 research outputs found
Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing
Recent developments in quaternion-valued widely linear processing have
established that the exploitation of complete second-order statistics requires
consideration of both the standard covariance and the three complementary
covariance matrices. Although such matrices have a tremendous amount of
structure and their decomposition is a powerful tool in a variety of
applications, the non-commutative nature of the quaternion product has been
prohibitive to the development of quaternion uncorrelating transforms. To this
end, we introduce novel techniques for a simultaneous decomposition of the
covariance and complementary covariance matrices in the quaternion domain,
whereby the quaternion version of the Takagi factorisation is explored to
diagonalise symmetric quaternion-valued matrices. This gives new insights into
the quaternion uncorrelating transform (QUT) and forms a basis for the proposed
quaternion approximate uncorrelating transform (QAUT) which simultaneously
diagonalises all four covariance matrices associated with improper quaternion
signals. The effectiveness of the proposed uncorrelating transforms is
validated by simulations on both synthetic and real-world quaternion-valued
signals.Comment: 41 pages, single column, 10 figure
Measurement of two independent phase-shifts using coupled parametric amplifiers
In this article, we demonstrate a scheme capable of two-phase measurement,
i.e. the simultaneous measurement of the two phase-shifts occurring in two
independent Mach-Zehnder interferometers using one intensity detector. Our
scheme utilizes dark-state-enhanced coupled parametric amplifiers in an atomic
medium to mix the multiple fields probing the various arms of the
interferometers in parallel. The two phase-differences are then encoded in
separate continuous-variable parameters in the spectral waveform of the
parametrically amplified atom-radiated signal field, which can be directly
decoupled in a single intensity measurement. Besides resolving two phase
differences in parallel, this method can also be used to increase the channel
capacity in optical and quantum communication by the simultaneous use of
phase-modulation and amplitude-modulation.Comment: 8 pages, 4 figure
Effective Vortex Mass from Microscopic Theory
We calculate the effective mass of a single quantized vortex in the BCS
superconductor at finite temperature. Based on effective action approach, we
arrive at the effective mass of a vortex as integral of the spectral function
divided by over frequency. The spectral function is
given in terms of the quantum-mechanical transition elements of the gradient of
the Hamiltonian between two Bogoliubov-deGennes (BdG) eigenstates. Based on
self-consistent numerical diagonalization of the BdG equation we find that the
effective mass per unit length of vortex at zero temperature is of order (=Fermi momentum, =coherence length), essentially
equaling the electron mass displaced within the coherence length from the
vortex core. Transitions between the core states are responsible for most of
the mass. The mass reaches a maximum value at and decreases
continuously to zero at .Comment: Supercedes prior version, cond-mat/990312
Generalized Stacking Fault Energy Surfaces and Dislocation Properties of Silicon: A First-Principles Theoretical Study
The generalized stacking fault (GSF) energy surfaces have received
considerable attention due to their close relation to the mechanical properties
of solids. We present a detailed study of the GSF energy surfaces of silicon
within the framework of density functional theory. We have calculated the GSF
energy surfaces for the shuffle and glide set of the (111) plane, and that of
the (100) plane of silicon, paying particular attention to the effects of the
relaxation of atomic coordinates. Based on the calculated GSF energy surfaces
and the Peierls-Nabarro model, we obtain estimates for the dislocation
profiles, core energies, Peierls energies, and the corresponding stresses for
various planar dislocations of silicon.Comment: 9 figures (not included; send requests to [email protected]
The Solar hep Process in Effective Field Theory
Using effective field theory, we calculate the S-factor for the hep process
in a totally parameter-free formulation. The transition operators are organized
according to chiral counting, and their matrix elements are evaluated using the
realistic nuclear wave functions obtained in the
correlated-hyperspherical-harmonics method. Terms of up to
next-to-next-to-next-to-leading order in heavy-baryon chiral perturbation
theory are considered. Fixing the only parameter in the theory by fitting the
tritium \beta-decay rate, we predict the hep S-factor with accuracy better than
\sim 20 %.Comment: 4 pages, Revtex. Minor revision has been mad
Parameter-Free Calculation of the Solar Proton Fusion Rate in Effective Field Theory
Spurred by the recent complete determination of the weak currents in
two-nucleon systems up to in heavy-baryon chiral perturbation
theory, we carry out a parameter-free calculation of the solar proton fusion
rate in an effective field theory that combines the merits of the standard
nuclear physics method and systematic chiral expansion. Using the tritium
beta-decay rate as an input to fix the only unknown parameter in the effective
Lagrangian, we can evaluate with drastically improved precision the ratio of
the two-body contribution to the well established one-body contribution; the
ratio is determined to be (0.86\pm 0.05) %. This result is essentially
independent of the cutoff parameter for a wide range of its variation (500 MeV
\le \Lambda \le 800 MeV), a feature that substantiates the consistency of the
calculation.Comment: 10 pages. The argument is considerably more sharpened with a reduced
error ba
Singlet superfield extension of the minimal supersymmetric standard model with Peccei-Quinn symmetry and a light pseudoscalar Higgs boson at the LHC
Motivated by the mu-problem and the axion solution to the strong CP-problem,
we extend the MSSM with one more chiral singlet field . The underlying
PQ-symmetry allows only one more term in the superpotential. The
spectrum of the Higgs system includes a light pseudoscalar (in addition
to the standard CP-even Higgs boson), predominantly decaying to two photons:
. Both Higgs bosons might be in the range accessible to
current LHC experiments.Comment: 5 pages with 3 figure
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