17,196 research outputs found
On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems
For a given subspace, the Rayleigh-Ritz method projects the large quadratic
eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar
to the Rayleigh-Ritz method for the linear eigenvalue problem, the
Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP
with respect to the projection subspace. We analyze the convergence of the
method when the angle between the subspace and the desired eigenvector
converges to zero. We prove that there is a Ritz value that converges to the
desired eigenvalue unconditionally but the Ritz vector converges conditionally
and may fail to converge. To remedy the drawback of possible non-convergence of
the Ritz vector, we propose a refined Ritz vector that is mathematically
different from the Ritz vector and is proved to converge unconditionally. We
construct examples to illustrate our theory.Comment: 20 page
Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator
The dependence of quantum correlation of twin beams on the pump finesse of an
optical parametric oscillator is studied with a semi-classical analysis. It is
found that the phase-sum correlation of the output signal and idler beams from
an optical parametric oscillator operating above threshold depends on the
finesse of the pump field when the spurious pump phase noise generated inside
the optical cavity and the excess noise of the input pump field are involved in
the Langevin equations. The theoretical calculations can explain the previously
experimental results, quantitatively.Comment: 27 pages, 8 figure
Distinguishing left- and right-handed molecules by two-step coherent pulses
Chiral molecules with broken parity symmetries can be modeled as quantum
systems with cyclic-transition structures. By using these novel properties, we
design two-step laser pulses to distinguish left- and right-handed molecules
from the enantiomers. After the applied pulse drivings, one kind chiral
molecules are trapped in coherent population trapping state, while the other
ones are pumped to the highest states for ionizations. Then, different chiral
molecules can be separated.Comment: 11 pages, 3 figures
Study on initial geometry fluctuations via participant plane correlations in heavy ion collisions: part II
Further investigation of the participant plane correlations within a Glauber
model framework is presented, focusing on correlations between three or four
participant planes of different order. A strong correlation is observed for
which is a reflection of the
elliptic shape of the overlap region. The correlation between the corresponding
experimental reaction plane angles can be easily measured. Strong correlations
of similar geometric origin are also observed for
,
,
,
,
, and
, which are also measurable.
Experimental measurements of the corresponding reaction plane correlators in
heavy ion collisions at RHIC and the LHC may improve our understanding of the
physics underlying the measured higher order flow harmonics.Comment: 5 pages, 5 figure
Appraising long-term regional climate policies in Inner Mongolia, the Tisza floodplain and the Guadiana river basin
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