Regular modes in rotating stars

Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray dynamics to build an asymptotic theory for the subset of regular modes which are the easiest to observe and identify. Comparisons with 2D numerical simulations of oscillations in polytropic stars show that both the frequency and amplitude distributions of these modes can accurately be described by an asymptotic theory for almost all rotation rates. The spectra are mainly characterized by two quantum numbers; their extraction from observed spectra should enable one to obtain information about stellar interiors.Comment: 5 pages, 4 figures, discussion adde

Projective dynamics and classical gravitation

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is a 2-plane containing the ray. Throwing the particle with a given initial impulsion defines a projective trajectory. It is a curve in the space of rays S(V), together with an impulsion attached to each ray. In the simplest example where the force is identically zero, the curve is a straight line and the impulsion a constant bivector. A striking feature of projective dynamics appears: the trajectories are not parameterized. Among the projective force fields corresponding to a central force, the one defining the Kepler problem is simpler than those corresponding to other homogeneities. Here the thrown ray describes a quadratic cone whose section by a hyperplane corresponds to a Keplerian conic. An original point of view on the hidden symmetries of the Kepler problem emerges, and clarifies some remarks due to Halphen and Appell. We also get the unexpected conclusion that there exists a notion of divergence-free field of projective forces if and only if dim V=4. No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure

Synthesis of Air-Stable CdSe/ZnS Core–Shell Nanoplatelets with Tunable Emission Wavelength

In the past few years, several protocols have been reported on the synthesis of CdSe nanoplatelets with narrow photoluminescence (PL) spectrum, high PL quantum efficiency, and short exciton lifetime. The corresponding core/shell nanoplatelets are however still mostly based on CdSe/CdS, which possess an extended lifetime and a strong red shift of the band-edge absorption and emission, in accordance with a quasi-type-II band alignment. Here we report on a robust synthesis procedure to grow a ZnS shell around CdSe nanoplatelets at moderate temperatures of 100–150 °C, to improve the optical properties of CdSe nanoplatelets via a type-I core/shell heterostructure. The shell growth is performed under ambient atmosphere, in either toluene or 1,2-dichlorobenzene. The variation of the shell thickness induces a continuous red shift of the PL peak, eventually reaching 611 nm. The PL quantum efficiency is increased compared to the original CdSe cores, with values up to 60% depending on the shell thickness. High-resolution transmission electron microscopy reveals a bending of the nanoplatelets caused by strain due to 12% lattice mismatch between CdSe and ZnS. The present procedure can easily be translated to other core/shell nanocrystals, such as CdSe/CdS and CdSe/CdZnS nanoplatelets.The present publication is realized with the support of the Ministero degli Affari Esteri e della Cooperazione Internazionale (IONX-NC4SOL). This project has also received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 696656 (GrapheneCore1). J.L.M. acknowledges support from UJI project P1-1B2014-24 and MINECO project CTQ2014-60178-P

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

Neutron scattering study of transverse magnetism

In order to clarify the nature of the additional phase transition at H1 (T) \u3c Hc (T) of the layered antiferromagnetic (AF) insulator FeBr2 as found by Aruga Katori et al. (1996) we measured the intensity of different Bragg-peaks in different scattering geometries. Transverse AF ordering is observed in both AF phases, AFI and AFII. Its order parameter exhibits a peak at T1 = T (H1) in temperature scans and does not vanish in zero field. Possible origins of the step-like increase of the transverse ferromagnetic ordering induced by a weak in-plane field component when entering AFI below T1 are discussed

Beyond the Standard "Marginalizations" of Wigner Function

We discuss the problem of finding "marginal" distributions within different tomographic approaches to quantum state measurement, and we establish analytical connections among them.Comment: 12 pages, LaTex, no figures, to appear in Quantum and Semiclass. Op

Relation between Barrier Conductance and Coulomb Blockade Peak Splitting for Tunnel-Coupled Quantum Dots

We study the relation between the barrier conductance and the Coulomb blockade peak splitting for two electrostatically equivalent dots connected by tunneling channels with bandwidths much larger than the dot charging energies. We note that this problem is equivalent to a well-known single-dot problem and present solutions for the relation between peak splitting and barrier conductance in both the weak and strong coupling limits. Results are in good qualitative agreement with the experimental findings of F. R. Waugh et al.Comment: 19 pages (REVTeX 3.0), 3 Postscript figure

Time-Dependent Invariants and Green's Functions in the Probability Representation of Quantum Mechanics

In the probability representation of quantum mechanics, quantum states are represented by a classical probability distribution, the marginal distribution function (MDF), whose time dependence is governed by a classical evolution equation. We find and explicitly solve, for a wide class of Hamiltonians, new equations for the Green's function of such an equation, the so-called classical propagator. We elucidate the connection of the classical propagator to the quantum propagator for the density matrix and to the Green's function of the Schr\"odinger equation. Within the new description of quantum mechanics we give a definition of coherence solely in terms of properties of the MDF and we test the new definition recovering well known results. As an application, the forced parametric oscillator is considered . Its classical and quantum propagator are found, together with the MDF for coherent and Fock states.Comment: 29 pages, RevTex, 6 eps-figures, to appear on Phys. Rev.