9,619 research outputs found
Hilbert-Schmidt Separability Probabilities and Noninformativity of Priors
The Horodecki family employed the Jaynes maximum-entropy principle, fitting
the mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by
Rajagopal by incorporating the dispersion (\sigma_{1}^2) of the observable, and
by Canosa and Rossignoli, by generalizing the observable (B_{\alpha}). We
further extend the Horodecki one-parameter model in both these manners,
obtaining a three-parameter (b_{1},\sigma_{1}^2,\alpha) two-qubit model, for
which we find a highly interesting/intricate continuum (-\infty < \alpha <
\infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the
golden ratio is featured. Our model can be contrasted with the three-parameter
(b_{q}, \sigma_{q}^2,q) one of Abe and Rajagopal, which employs a
q(Tsallis)-parameter rather than , and has simply q-invariant HS
separability probabilities of 1/2. Our results emerge in a study initially
focused on embedding certain information metrics over the two-level quantum
systems into a q-framework. We find evidence that Srednicki's recently-stated
biasedness criterion for noninformative priors yields rankings of priors fully
consistent with an information-theoretic test of Clarke, previously applied to
quantum systems by Slater.Comment: 26 pages, 12 figure
From presence to consciousness through virtual reality
Immersive virtual environments can break the deep, everyday connection between where our senses tell us we are and where we are actually located and whom we are with. The concept of 'presence' refers to the phenomenon of behaving and feeling as if we are in the virtual world created by computer displays. In this article, we argue that presence is worthy of study by neuroscientists, and that it might aid the study of perception and consciousness
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
On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere
Single variable hypergeometric functions pFq arise in connection with the
power series solution of the Schrodinger equation or in the summation of
perturbation expansions in quantum mechanics. For these applications, it is of
interest to obtain analytic expressions, and we present the reduction of a
number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related
series have additional applications in quantum and statistical physics and
chemistry.Comment: 17 pages, no figure
A massive Feynman integral and some reduction relations for Appell functions
New explicit expressions are derived for the one-loop two-point Feynman
integral with arbitrary external momentum and masses and in D
dimensions. The results are given in terms of Appell functions, manifestly
symmetric with respect to the masses . Equating our expressions with
previously known results in terms of Gauss hypergeometric functions yields
reduction relations for the involved Appell functions that are apparently new
mathematical results.Comment: 19 pages. To appear in Journal of Mathematical Physic
Homogenization induced by chaotic mixing and diffusion in an oscillatory chemical reaction
A model for an imperfectly mixed batch reactor with the chlorine dioxide-iodine-malonic acid (CDIMA) reaction, with the mixing being modelled by chaotic advection, is considered. The reactor is assumed to be operating in oscillatory mode and the way in which an initial spatial perturbation becomes homogenized is examined. When the kinetics are such that the only stable homogeneous state is oscillatory then the perturbation is always entrained into these oscillations. The rate at which this occurs is relatively insensitive to the chemical effects, measured by the Damkohler number, and is comparable to the rate of homogenization of a passive contaminant. When both steady and oscillatory states are stable, spatially homogeneous states, two possibilities can occur. For the smaller Damkohler numbers, a localized perturbation at the steady state is homogenized within the background oscillations. For larger Damkohler numbers, regions of both oscillatory and steady behavior can co-exist for relatively long times before the system collapses to having the steady state everywhere. An interpretation of this behavior is provided by the one-dimensional Lagrangian filament model, which is analyzed in detail
Ground state of two electrons on concentric spheres
We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79},
062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on
concentric spheres with different radii. The strengths and weaknesses of
several electronic structure models are analyzed, ranging from the mean-field
approximation (restricted and unrestricted Hartree-Fock solutions) to
configuration interaction expansion, leading to near-exact wave functions and
energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the
asymptotic expansion for the large-spheres regime are also considered. We also
study the position intracules derived from approximate and exact wave
functions. We find evidence for the existence of a long-range Coulomb hole in
the large-spheres regime, and infer that unrestricted Hartree-Fock theory
over-localizes the electrons.Comment: 10 pages, 10 figure
Bures distance between two displaced thermal states
The Bures distance between two displaced thermal states and the corresponding
geometric quantities (statistical metric, volume element, scalar curvature) are
computed. Under nonunitary (dissipative) dynamics, the statistical distance
shows the same general features previously reported in the literature by
Braunstein and Milburn for two--state systems. The scalar curvature turns out
to have new interesting properties when compared to the curvature associated
with squeezed thermal states.Comment: 3 pages, RevTeX, no figure
Solving the two-center nuclear shell-model problem with arbitrarily-orientated deformed potentials
A general new technique to solve the two-center problem with
arbitrarily-orientated deformed realistic potentials is demonstrated, which is
based on the powerful potential separable expansion method. As an example,
molecular single-particle spectra for C + C Mg are
calculated using deformed Woods-Saxon potentials. These clearly show that
non-axial symmetric configurations play a crucial role in molecular resonances
observed in reaction processes for this system at low energy
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