9,892 research outputs found
A priori probability that a qubit-qutrit pair is separable
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems)
and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181),
which was concerned with the simplest instance of entangled quantum systems,
pairs of qubits. As in that analysis -- again on the basis of numerical
(quasi-Monte Carlo) integration results, but now in a still higher-dimensional
space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical
distinguishability) probability that arbitrarily paired qubits and qutrits are
separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where
u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive
primes). This is considerably less than the conjectured value of the Bures/SD
probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these
conjectures, in turn, rely upon ones to the effect that the SD volumes of
separable states assume certain remarkable forms, involving "primorial"
numbers. We also estimate the SD area of the boundary of separable qubit-qutrit
states, and provide preliminary calculations of the Bures/SD probability of
separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact
computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures
volume of mixed quantum states" to refine our conjecture
Volume of the quantum mechanical state space
The volume of the quantum mechanical state space over -dimensional real,
complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean
measure is computed, and explicit formulas are presented for the expected value
of the determinant in the general setting too. The case when the state space is
endowed with a monotone metric or a pull-back metric is considered too, we give
formulas to compute the volume of the state space with respect to the given
Riemannian metric. We present the volume of the space of qubits with respect to
various monotone metrics. It turns out that the volume of the space of qubits
can be infinite too. We characterize those monotone metrics which generates
infinite volume.Comment: 17 page
Molecular Gas, Dust and Star Formation in Galaxies: II. Dust properties and scalings in \sim\ 1600 nearby galaxies
We aim to characterize the relationship between dust properties. We also aim
to provide equations to estimate accurate dust properties from limited
observational datasets.
We assemble a sample of 1,630 nearby (z<0.1) galaxies-over a large range of
Mstar, SFR - with multi-wavelength observations available from wise, iras,
planck and/or SCUBA. The characterization of dust emission comes from SED
fitting using Draine & Li dust models, which we parametrize using two
components (warm and cold ). The subsample of these galaxies with global
measurements of CO and/or HI are used to explore the molecular and/or atomic
gas content of the galaxies.
The total Lir, Mdust and dust temperature of the cold component (Tc) form a
plane that we refer to as the dust plane. A galaxy's sSFR drives its position
on the dust plane: starburst galaxies show higher Lir, Mdust and Tc compared to
Main Sequence and passive galaxies. Starburst galaxies also show higher
specific Mdust (Mdust/Mstar) and specific Mgas (Mgas/Mstar). The Mdust is more
closely correlated with the total Mgas (atomic plus molecular) than with the
individual components. Our multi wavelength data allows us to define several
equations to estimate Lir, Mdust and Tc from one or two monochromatic
luminosities in the infrared and/or sub-millimeter.
We estimate the dust mass and infrared luminosity from a single monochromatic
luminosity within the R-J tail of the dust emission, with errors of 0.12 and
0.20dex, respectively. These errors are reduced to 0.05 and 0.10 dex,
respectively, if the Tc is used. The Mdust is correlated with the total Mism
(Mism \propto Mdust^0.7). For galaxies with Mstar 8.5<log(Mstar/Msun) < 11.9,
the conversion factor \alpha_850mum shows a large scatter (rms=0.29dex). The SF
mode of a galaxy shows a correlation with both the Mgass and Mdust: high
Mdust/Mstar galaxies are gas-rich and show the highest SFRs.Comment: 24 pages, 28 figures, 6 tables, Accepted for publication in A&
Finite-level systems, Hermitian operators, isometries, and a novel parameterization of Stiefel and Grassmann manifolds
In this paper we obtain a description of the Hermitian operators acting on
the Hilbert space \C^n, description which gives a complete solution to the
over parameterization problem. More precisely we provide an explicit
parameterization of arbitrary -dimensional operators, operators that may be
considered either as Hamiltonians, or density matrices for finite-level quantum
systems. It is shown that the spectral multiplicities are encoded in a flag
unitary matrix obtained as an ordered product of special unitary matrices, each
one generated by a complex -dimensional unit vector, . As a
byproduct, an alternative and simple parameterization of Stiefel and Grassmann
manifolds is obtained.Comment: 21 page
On the ab initio calculation of CVV Auger spectra in closed-shell systems
We propose an ab initio method to evaluate the core-valence-valence (CVV)
Auger spectrum of systems with filled valence bands. The method is based on the
Cini-Sawatzky theory, and aims at estimating the parameters by first-principles
calculations in the framework of density-functional theory (DFT). Photoemission
energies and the interaction energy for the two holes in the final state are
evaluated by performing DFT simulations for the system with varied population
of electronic levels. Transition matrix elements are taken from atomic results.
The approach takes into account the non-sphericity of the density of states of
the emitting atom, spin-orbit interaction in core and valence, and non
quadratic terms in the total energy expansion with respect to fractional
occupation numbers. It is tested on two benchmark systems, Zn and Cu metals,
leading in both cases to L23M45M45 Auger peaks within 2 eV from the
experimental ones. Detailed analysis is presented on the relative weight of the
various contributions considered in our method, providing the basis for future
development. Especially problematic is the evaluation of the hole-hole
interaction for systems with broad valence bands: our method underestimates its
value in Cu, while we obtain excellent results for this quantity in Zn.Comment: 20 pages, 5 figures, 4 table
Rydberg transition frequencies from the Local Density Approximation
A method is given that extracts accurate Rydberg excitations from LDA density
functional calculations, despite the short-ranged potential. For the case of He
and Ne, the asymptotic quantum defects predicted by LDA are in less than 5%
error, yielding transition frequency errors of less than 0.1eV.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let
Broad-band polarization-independent total absorption of electromagnetic waves by an overdense plasma
We have shown both experimentally and theoretically that
polarization-independent broad-band absorption of electromagnetic waves by an
overdense plasma, caused by surface plasmon-polaritons (SPP) excitation, can be
achieved due to combination of two factors: a non-zero angle of incidence and a
two-dimensional circular diffraction grating placed at a properly chosen
distance in front of the plasma boundary. Direct detection of SPP has been
achieved for the first time using a miniature antenna imbedded in the plasma.Comment: considerably broadened versio
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
We report the results of certain integrations of quantum-theoretic interest,
relying, in this regard, upon recently developed parameterizations of Boya et
al of the n x n density matrices, in terms of squared components of the unit
(n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized
volume elements of the Bures (minimal monotone) metric for n = 2 and 3,
obtaining thereby "Bures prior probability distributions" over the two- and
three-state systems. Then, as an essential first step in extending these
results to n > 3, we determine that the "Hall normalization constant" (C_{n})
for the marginal Bures prior probability distribution over the
(n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices
is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it
follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known
to equal 2/pi.) The constant C_{5} is also found. It too is associated with a
remarkably simple decompositon, involving the product of the eight consecutive
prime numbers from 2 to 23.
We also preliminarily investigate several cases, n > 5, with the use of
quasi-Monte Carlo integration. We hope that the various analyses reported will
prove useful in deriving a general formula (which evidence suggests will
involve the Bernoulli numbers) for the Hall normalization constant for
arbitrary n. This would have diverse applications, including quantum inference
and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in
J. Phys. A. We make a few slight changes from the previous version, but also
add a subsection (III G) in which several variations of the basic problem are
newly studied. Rather strong evidence is adduced that the Hall constants are
related to partial sums of denominators of the even-indexed Bernoulli
numbers, although a general formula is still lackin
Majorana solutions to the two-electron problem
A review of the known different methods and results devised to study the
two-electron atom problem, appeared in the early years of quantum mechanics, is
given, with particular reference to the calculations of the ground state energy
of helium. This is supplemented by several, unpublished results obtained around
the same years by Ettore Majorana, which results did not convey in his
published papers on the argument, and thus remained unknown until now.
Particularly interesting, even for current research in atomic and nuclear
physics, is a general variant of the variational method, developed by Majorana
in order to take directly into account, already in the trial wavefunction, the
action of the full Hamiltonian operator of a given quantum system. Moreover,
notable calculations specialized to the study of the two-electron problem show
the introduction of the remarkable concept of an effective nuclear charge
different for the two electrons (thus generalizing previous known results), and
an application of the perturbative method, where the atomic number Z was
treated effectively as a continuous variable, contributions to the ground state
energy of an atom with given Z coming also from any other Z. Instead,
contributions relevant mainly for pedagogical reasons count simple broad range
estimates of the helium ionization potential, obtained by suitable choices for
the wavefunction, as well as a simple alternative to Hylleraas' method, which
led Majorana to first order calculations comparable in accuracy with well-known
order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure
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