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 $D$-dimensional hydrogenic and oscillator-like systems, the wavefunctions of the corresponding bound states are controlled by the Laguerre ($\mathcal{L}_{m}^{(\alpha)}(x)$) and Gegenbauer ($\mathcal{C}^{(\alpha)}_{m}(x)$) polynomials in both position and momentum spaces, where the parameter $\alpha$ linearly depends on $D$. In this work we study the asymptotic behavior as $\alpha \to \infty$ 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) $\chi^2$ test for distinguishing two quantum states gives rise to the quantum $\chi^2$ 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 Schr$\ddot{o}$dinger equation with the Hulth$\acute{e}$n potential plus ring-shape potential for $\ell\neq 0$ 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 Hulth$\acute{e}$n 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