731 research outputs found
Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters
The determination of the physical entropies (R\'enyi, Shannon, Tsallis) of
high-dimensional quantum systems subject to a central potential requires the
knowledge of the asymptotics of some power and logarithmic integral functionals
of the hypergeometric orthogonal polynomials which control the wavefunctions of
the stationary states. For the -dimensional hydrogenic and oscillator-like
systems, the wavefunctions of the corresponding bound states are controlled by
the Laguerre () and Gegenbauer
() polynomials in both position and momentum
spaces, where the parameter linearly depends on . In this work we
study the asymptotic behavior as of the associated
entropy-like integral functionals of these two families of hypergeometric
polynomials
Reproducibility and validity of a diet quality index for children assessed using a FFQ
The diet quality index (DQI) for preschool children is a new index developed to reflect compliance with four main food-based dietary guidelines for preschool children in Flanders. The present study investigates: (1) the validity of this index by comparing DQI scores for preschool children with nutrient intakes, both of which were derived from 3d estimated diet records; (2) the reproducibility of the DQI for preschoolers based on a parentally reported forty-seven-item FFQ DQI, which was repeated after 5 weeks; (3) the relative validity of the FFQ DQI with 3d record DQI scores as reference. The study sample included 510 and 58 preschoolers (2-5-6.5 years) for validity and reproducibility analyses, respectively. Increasing 3d record DQI scores were associated with decreasing consumption of added sugars, and increasing intakes of fibre, water, Ca and many micronutrients. Mean FFQ DQI test-retest scores were not significantly different: 72 (so 11) v. 71 (Si) 10) (P-=0-218) out of a maximum of 100. Mean 3d record DQI score (66 (so 10)) was significantly lower than mean FFQ DQI (71 (so 10);
Landau-Zener-St\"uckelberg interferometry in pair production from counterpropagating lasers
The rate of electron-positron pair production in linearly polarized
counter-propagating lasers is evaluated from a recently discovered solution of
the time-dependent Dirac equation. The latter is solved in momentum space where
it is formally equivalent to the Schr\"odinger equation describing a strongly
driven two-level system. The solution is found from a simple transformation of
the Dirac equation and is given in compact form in terms of the
doubly-confluent Heun's function. By using the analogy with the two-level
system, it is shown that for high-intensity lasers, pair production occurs
through periodic non-adiabatic transitions when the adiabatic energy gap is
minimal. These transitions give rise to an intricate interference pattern in
the pair spectrum, reminiscent of the Landau-Zener-St\"uckelberg phenomenon in
molecular physics: the accumulated phase result in constructive or destructive
interference. The adiabatic-impulse model is used to study this phenomenon and
shows an excellent agreement with the exact result.Comment: 22 pages, 7 figure
Crossover between ballistic and diffusive transport: The Quantum Exclusion Process
We study the evolution of a system of free fermions in one dimension under
the simultaneous effects of coherent tunneling and stochastic Markovian noise.
We identify a class of noise terms where a hierarchy of decoupled equations for
the correlation functions emerges. In the special case of incoherent,
nearest-neighbour hopping the equation for the two-point functions is solved
explicitly. The Green's function for the particle density is obtained
analytically and a timescale is identified where a crossover from ballistic to
diffusive behaviour takes place. The result can be interpreted as a competition
between the two types of conduction channels where diffusion dominates on large
timescales.Comment: 20 pages, 5 figure
UCN Upscattering rates in a molecular deuterium crystal
A calculation of ultra-cold neutron (UCN) upscattering rates in molecular
deuterium solids has been carried out, taking into account intra-molecular
exictations and phonons. The different moelcular species ortho-D2 (with even
rotational quantum number J) and para-D2 (with odd J) exhibit significantly
different UCN-phonon annihilation cross-sections. Para- to ortho-D2 conversion,
furthermore, couples UCN to an energy bath of excited rotational states without
mediating phonons. This anomalous upscattering mechanism restricts the UCN
lifetime to 4.6 msec in a normal-D2 solid with 33% para content.Comment: 3 pages, one figur
Quantum Chi-Squared and Goodness of Fit Testing
The density matrix in quantum mechanics parameterizes the statistical
properties of the system under observation, just like a classical probability
distribution does for classical systems. The expectation value of observables
cannot be measured directly, it can only be approximated by applying classical
statistical methods to the frequencies by which certain measurement outcomes
(clicks) are obtained. In this paper, we make a detailed study of the
statistical fluctuations obtained during an experiment in which a hypothesis is
tested, i.e. the hypothesis that a certain setup produces a given quantum
state. Although the classical and quantum problem are very much related to each
other, the quantum problem is much richer due to the additional optimization
over the measurement basis. Just as in the case of classical hypothesis
testing, the confidence in quantum hypothesis testing scales exponentially in
the number of copies. In this paper, we will argue 1) that the physically
relevant data of quantum experiments is only contained in the frequencies of
the measurement outcomes, and that the statistical fluctuations of the
experiment are essential, so that the correct formulation of the conclusions of
a quantum experiment should be given in terms of hypothesis tests, 2) that the
(classical) test for distinguishing two quantum states gives rise to
the quantum divergence when optimized over the measurement basis, 3)
present a max-min characterization for the optimal measurement basis for
quantum goodness of fit testing, find the quantum measurement which leads both
to the maximal Pitman and Bahadur efficiency, and determine the associated
divergence rates.Comment: 22 Pages, with a new section on parameter estimatio
The Schrodinger equation with Hulthen potential plus ring-shaped potential
We present the solutions of the Schrdinger equation with the
Hulthn potential plus ring-shape potential for states
within the framework of an exponential approximation of the centrifugal
potential.Solutions to the corresponding angular and radial equations are
obtained in terms of special functions using the conventional Nikiforov-Uvarov
method. The normalization constant for the Hulthn potential is also
computed.Comment: Typed with LateX,12 Pages, Typos correcte
High-throughput phenotyping of pea physiological traits for drought stress tolerance
info:eu-repo/semantics/publishedVersio
Rapid mixing implies exponential decay of correlations
We provide an analysis of the correlation properties of spin and fermionic
systems on a lattice evolving according to open system dynamics generated by a
local primitive Liouvillian. We show that if the Liouvillian has a spectral gap
which is independent of the system size, then the correlations between local
observables decay exponentially as a function of the distance between their
supports. We prove, furthermore, that if the Log-Sobolev constant is
independent of the system size, then the system satisfies clustering of
correlations in the mutual information - a much more stringent form of
correlation decay. As a consequence, in the latter case we get an area law
(with logarithmic corrections) for the mutual information. As a further
corollary, we obtain a stability theorem for local distant perturbations. We
also demonstrate that gapped free-fermionic systems exhibit clustering of
correlations in the covariance and in the mutual information. We conclude with
a discussion of the implications of these results for the classical simulation
of open quantum systems with matrix-product operators and the robust
dissipative preparation of topologically ordered states of lattice spin
systems.Comment: 25 pages, 2 figures, replaced by final versio
Are relativistic effects significant for the analysis of whistler-mode waves in the earth's magnetosphere?
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