Classical statistical distributions can violate Bell-type inequalities

We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles' angular momenta along axes with different orientations. It is shown that for certain observables, the correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the counterfactual event that plays a prominent role in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.Comment: v3: Extended version. To be published in J. Phys.

Contribution of forbidden orbits in the photoabsorption spectra of atoms and molecules in a magnetic field

In a previous work [Phys. Rev. A \textbf{66}, 0134XX (2002)] we noted a partial disagreement between quantum R-matrix and semiclassical calculations of photoabsorption spectra of molecules in a magnetic field. We show this disagreement is due to a non-vanishing contribution of processes which are forbidden according to the usual semiclassical formalism. Formulas to include these processes are obtained by using a refined stationary phase approximation. The resulting higher order in $\hbar$ contributions also account for previously unexplained ``recurrences without closed-orbits''. Quantum and semiclassical photoabsorption spectra for Rydberg atoms and molecules in a magnetic field are calculated and compared to assess the validity of the first-order forbidden orbit contributions.Comment: 12 pages, 6 figure

Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajectories follow the streamlines of the probability flow and are generically non-classical. This can also hold even for short times, when the wavepacket is still localized along a classical trajectory. This generic feature of Bohmian trajectories is expected to hold in the classical limit. We further argue that in this context decoherence cannot constitute a viable solution in order to recover classicality.Comment: Figures downgraded to low resolution; To be published in Found. Phys. (2009)

Observation of diffractive orbits in the spectrum of excited NO in a magnetic field

We investigate the experimental spectra of excited NO molecules in the diamagnetic regime and develop a quantitative semiclassical framework to account for the results. We show the dynamics can be interpreted in terms of classical orbits provided that in addition to the geometric orbits, diffractive effects are appropriately taken into account. We also show how individual orbits can be extracted from the experimental signal and use this procedure to reveal the first experimental manifestation of inelastic diffractive orbits.Comment: 4 fig

Molecules in external fields: a semiclassical analysis

We undertake a semiclassical analysis of the spectral properties (modulations of photoabsorption spectra, energy level statistics) of a simple Rydberg molecule in static fields within the framework of Closed-Orbit/Periodic-Orbit theories. We conclude that in addition to the usual classically allowed orbits one must consider classically forbidden diffractive paths. Further, the molecule brings in a new type of 'inelastic' diffractive trajectory, different from the usual 'elastic' diffractive orbits encountered in previous studies of atomic and analogous systems such as billiards with point-scatterers. The relative importance of inelastic versus elastic diffraction is quantified by merging the usual Closed Orbit theory framework with molecular quantum defect theory.Comment: 4 pages, 3 figure

Realism and the wave-function

Realism -- the idea that the concepts in physical theories refer to 'things' existing in the real world -- is introduced as a tool to analyze the status of the wave-function. Although the physical entities are recognized by the existence of invariant quantities, examples from classical and quantum physics suggest that not all the theoretical terms refer to the entities: some terms refer to properties of the entities, and some terms have only an epistemic function. In particular, it is argued that the wave-function may be written in terms of classical non-referring and epistemic terms. The implications for realist interpretations of quantum mechanics and on the teaching of quantum physics are examined.Comment: No figure

Nonparametric instrumental regression with non-convex constraints

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, like integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition

Non-Hermitian quantum mechanics: the case of bound state scattering theory

Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert spaces and metric operator relevant to a correct formulation of such theories. The structure and tools employed are the same that have been introduced in current works dealing with PT-symmetric and quasi-Hermitian problems. The relevance of the non-Hermitian formulation to practical computations is assessed by introducing a non-Hermiticity index. We give a numerical example involving scattering by a short-range potential in a Coulomb field for which it is seen that even for a small but non-negligible non-Hermiticity index the non-Hermitian character of the problem must be taken into account. The computation of physical quantities in the relevant Hilbert spaces is also discussed

Generalized Hamiltonian structures for Ermakov systems

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations, the existence of Casimir functions can give rise to superintegrable Ermakov systems. Finally, we characterize the cases where linearization of the equations of motion is possible

Variation in life history traits and transcriptome associated with adaptation to diet shifts in the ladybird Cryptolaemus montrouzieri

Background: Despite the broad diet range of many predatory ladybirds, the mechanisms involved in their adaptation to diet shifts are not completely understood. Here, we explored how a primarily coccidophagous ladybird Cryptolaemus montrouzieri adapts to feeding on aphids. Results: Based on the lower survival rate, longer developmental time, and lower adult body weight and reproduction rate of the predator, the aphid Megoura japonica proved being less suitable to support C. montrouzieri as compared with the citrus mealybug Planococcus citri. The results indicated up-regulation of genes related to ribosome and translation in fourth instars, which may be related to their suboptimal development. Also, several genes related to biochemical transport and metabolism, and detoxification were up-regulated as a result of adaptation to the changes in nutritional and non-nutritional (toxic) components of the prey. Conclusion: Our results indicated that C. montrouzieri succeeded in feeding on aphids by regulation of genes related to development, digestion and detoxification. Thus, we argue that these candidate genes are valuable for further studies of the functional evolution of ladybirds led by diet shifts