6,412 research outputs found
Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional
and 15-dimensional in nature, respectively. The total volumes of the spaces
they occupy with respect to the Hilbert-Schmidt and Bures metrics are
obtainable as special cases of formulas of Zyczkowski and Sommers. We claim
that if one could determine certain metric-independent 3-dimensional
"eigenvalue-parameterized separability functions" (EPSFs), then these formulas
could be readily modified so as to yield the Hilbert-Schmidt and Bures volumes
occupied by only the separable two-qubit states (and hence associated
separability probabilities). Motivated by analogous earlier analyses of
"diagonal-entry-parameterized separability functions", we further explore the
possibility that such 3-dimensional EPSFs might, in turn, be expressible as
univariate functions of some special relevant variable--which we hypothesize to
be the maximal concurrence (0 < C <1) over spectral orbits. Extensive numerical
results we obtain are rather closely supportive of this hypothesis. Both the
real and complex estimated EPSFs exhibit clearly pronounced jumps of magnitude
roughly 50% at C=1/2, as well as a number of additional matching
discontinuities.Comment: 12 pages, 7 figures, new abstract, revised for J. Phys.
Band Distributions for Quantum Chaos on the Torus
Band distributions (BDs) are introduced describing quantization in a toral
phase space. A BD is the uniform average of an eigenstate phase-space
probability distribution over a band of toral boundary conditions. A general
explicit expression for the Wigner BD is obtained. It is shown that the Wigner
functions for {\em all} of the band eigenstates can be reproduced from the
Wigner BD. Also, BDs are shown to be closer to classical distributions than
eigenstate distributions. Generalized BDs, associated with sets of adjacent
bands, are used to extend in a natural way the Chern-index characterization of
the classical-quantum correspondence on the torus to arbitrary rational values
of the scaled Planck constant.Comment: 12 REVTEX page
Advances in delimiting the Hilbert-Schmidt separability probability of real two-qubit systems
We seek to derive the probability--expressed in terms of the Hilbert-Schmidt
(Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit
system is separable, by implementing the well-known Peres-Horodecki test on the
partial transposes (PT's) of the associated 4 x 4 density matrices). But the
full implementation of the test--requiring that the determinant of the PT be
nonnegative for separability to hold--appears to be, at least presently,
computationally intractable. So, we have previously implemented--using the
auxiliary concept of a diagonal-entry-parameterized separability function
(DESF)--the weaker implied test of nonnegativity of the six 2 x 2 principal
minors of the PT. This yielded an exact upper bound on the separability
probability of 1024/{135 pi^2} =0.76854$. Here, we piece together
(reflection-symmetric) results obtained by requiring that each of the four 3 x
3 principal minors of the PT, in turn, be nonnegative, giving an
improved/reduced upper bound of 22/35 = 0.628571. Then, we conclude that a
still further improved upper bound of 1129/2100 = 0.537619 can be found by
similarly piecing together the (reflection-symmetric) results of enforcing the
simultaneous nonnegativity of certain pairs of the four 3 x 3 principal minors.
In deriving our improved upper bounds, we rely repeatedly upon the use of
certain integrals over cubes that arise. Finally, we apply an independence
assumption to a pair of DESF's that comes close to reproducing our numerical
estimate of the true separability function.Comment: 16 pages, 9 figures, a few inadvertent misstatements made near the
end are correcte
The Isotopic Composition of Strontium in Fossils from the Kendrick Shale, Kentucky
Author Institution: Department of Geology and Mineralogy, The Ohio State UniversityNine analyses of the isotopic composition of strontium in the carbonate shells of marine fossils from the Kendrick Shale (Lower Pennsylvanian) of Kentucky indicate an average 87Sr/86Sr ratio of 0.7086^O.OOOSS at the 95 percent confidence limit. This value is in satisfactory agreement with previous measurements by Peterman et al. (1970) and confirms that strontium in the oceans during Early Pennsylvanian time was anomalously enriched in radiogenic 87Sr, compared to that in earlier and later periods. The isotopic composition of strontium in skeletal clacium carbonate of cephalopods, gastropods, and brachiopods from the Kendrick Shale appears to be the same in spite of the different feeding habits of these animals
Qubit-Qutrit Separability-Probability Ratios
Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for
the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to
high numerical accuracy, the formulas of Sommers and Zyczkowski
(quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional
hyperarea of the (separable and nonseparable) N x N density matrices, based on
the Bures (minimal monotone) metric -- and also their analogous formulas
(quant-ph/0302197) for the (non-monotone) Hilbert-Schmidt metric. With the same
seven billion well-distributed (``low-discrepancy'') sample points, we estimate
the unknown volumes and hyperareas based on five additional (monotone) metrics
of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate
all of these seven volume and seven hyperarea (unknown) quantities when
restricted to the separable density matrices. The ratios of separable volumes
(hyperareas) to separable plus nonseparable volumes (hyperareas) yield
estimates of the separability probabilities of generically rank-six (rank-five)
density matrices. The (rank-six) separability probabilities obtained based on
the 35-dimensional volumes appear to be -- independently of the metric (each of
the seven inducing Haar measure) employed -- twice as large as those (rank-five
ones) based on the 34-dimensional hyperareas. Accepting such a relationship, we
fit exact formulas to the estimates of the Bures and Hilbert-Schmidt separable
volumes and hyperareas.(An additional estimate -- 33.9982 -- of the ratio of
the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite
clearly close to integral too.) The doubling relationship also appears to hold
for the N=4 case for the Hilbert-Schmidt metric, but not the others. We fit
exact formulas for the Hilbert-Schmidt separable volumes and hyperareas.Comment: 36 pages, 15 figures, 11 tables, final PRA version, new last
paragraph presenting qubit-qutrit probability ratios disaggregated by the two
distinct forms of partial transpositio
Ultrafast filling of an electronic pseudogap in an incommensurate crystal
We investigate the quasiperiodic crystal (LaS)1.196(VS2) by angle and time
resolved photoemission spectroscopy. The dispersion of electronic states is in
qualitative agreement with band structure calculated for the VS2 slab without
the incommensurate distortion. Nonetheless, the spectra display a temperature
dependent pseudogap instead of quasiparticles crossing. The sudden
photoexcitation at 50 K induces a partial filling of the electronic pseudogap
within less than 80 fs. The electronic energy flows into the lattice modes on a
comparable timescale. We attribute this surprisingly short timescale to a very
strong electron-phonon coupling to the incommensurate distortion. This result
sheds light on the electronic localization arising in aperiodic structures and
quasicrystals
Probing the Slope of Cluster Mass Profile with Gravitational Einstein Rings: Application to Abell 1689
The strong lensing modelling of gravitational ``rings'' formed around massive
galaxies is sensitive to the amplitude of the external shear and convergence
produced by nearby mass condensations. In current wide field surveys, it is now
possible to find out a large number of rings, typically 10 gravitational rings
per square degree. We propose here, to systematically study gravitational rings
around galaxy clusters to probe the cluster mass profile beyond the cluster
strong lensing regions. For cluster of galaxies with multiple arc systems, we
show that rings found at various distances from the cluster centre can improve
the modelling by constraining the slope of the cluster mass profile. We outline
the principle of the method with simple numerical simulations and we apply it
to 3 rings discovered recently in Abell~1689. In particular, the lens modelling
of the 3 rings confirms that the cluster is bimodal, and favours a slope of the
mass profile steeper than isothermal at a cluster radius \sim 300 \kpc. These
results are compared with previous lens modelling of Abell~1689 including weak
lensing analysis. Because of the difficulty arising from the complex mass
distribution in Abell~1689, we argue that the ring method will be better
implemented on simpler and relaxed clusters.Comment: Accepted for publication in MNRAS. Substantial modification after
referee's repor
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