Loschmidt Echo and Lyapunov Exponent in a Quantum Disordered System

We investigate the sensitivity of a disordered system with diffractive scatterers to a weak external perturbation. Specifically, we calculate the fidelity M(t) (also called the Loschmidt echo) characterizing a return probability after a propagation for a time $t$ followed by a backward propagation governed by a slightly perturbed Hamiltonian. For short-range scatterers we perform a diagrammatic calculation showing that the fidelity decays first exponentially according to the golden rule, and then follows a power law governed by the diffusive dynamics. For long-range disorder (when the diffractive scattering is of small-angle character) an intermediate regime emerges where the diagrammatics is not applicable. Using the path integral technique, we derive a kinetic equation and show that M(t) decays exponentially with a rate governed by the classical Lyapunov exponent.Comment: 9 pages, 7 figure

Universality of the Lyapunov regime for the Loschmidt echo

The Loschmidt echo (LE) is a magnitude that measures the sensitivity of quantum dynamics to perturbations in the Hamiltonian. For a certain regime of the parameters, the LE decays exponentially with a rate given by the Lyapunov exponent of the underlying classically chaotic system. We develop a semiclassical theory, supported by numerical results in a Lorentz gas model, which allows us to establish and characterize the universality of this Lyapunov regime. In particular, the universality is evidenced by the semiclassical limit of the Fermi wavelength going to zero, the behavior for times longer than Ehrenfest time, the insensitivity with respect to the form of the perturbation and the behavior of individual (non-averaged) initial conditions. Finally, by elaborating a semiclassical approximation to the Wigner function, we are able to distinguish between classical and quantum origin for the different terms of the LE. This approach renders an understanding for the persistence of the Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our results in terms of the quantum--classical transition.Comment: 33 pages, 17 figures, uses Revtex

On subducting slab entrainment of buoyant asthenosphere

Laboratory and numerical experiments and boundary layer analysis of the entrainment of buoyant asthenosphere by subducting oceanic lithosphere implies that slab entrainment is likely to be relatively inefficient at removing a buoyant and lower viscosity asthenosphere layer. Asthenosphere would instead be mostly removed by accretion into and eventual subduction of the overlying oceanic lithosphere. The lower (hot) side of a subducting slab entrains by the formation of a ∼10–30 km-thick downdragged layer, whose thickness depends upon the subduction rate and the density contrast and viscosity of the asthenosphere, while the upper (cold) side of the slab may entrain as much by thermal 'freezing' onto the slab as by mechanical downdragging. This analysis also implies that proper treatment of slab entrainment in future numerical mantle flow experiments will require the resolution of ∼10–30 km-thick entrainment boundary layers

Short-range interactions in a two-electron system: energy levels and magnetic properties

The problem of two electrons in a square billiard interacting via a finite-range repulsive Yukawa potential and subjected to a constant magnetic field is considered. We compute the energy spectrum for both singlet and triplet states, and for all symmetry classes, as a function of the strength and range of the interaction and of the magnetic field. We show that the short-range nature of the potential suppresses the formation of ``Wigner molecule'' states for the ground state, even in the strong interaction limit. The magnetic susceptibility $\chi(B)$ shows low-temperature paramagnetic peaks due to exchange induced singlet-triplet oscillations. The position, number and intensity of these peaks depend on the range and strength of the interaction. The contribution of the interaction to the susceptibility displays paramagnetic and diamagnetic phases as a function of $T$.Comment: 12 pages,6 figures; to appear in Phys. Rev.

Mode structure and ray dynamics of a parabolic dome microcavity

We consider the wave and ray dynamics of the electromagnetic field in a parabolic dome microcavity. The structure of the fundamental s-wave involves a main lobe in which the electromagnetic field is confined around the focal point in an effective volume of the order of a cubic wavelength, while the modes with finite angular momentum have a structure that avoids the focal area and have correspondingly larger effective volume. The ray dynamics indicates that the fundamental s-wave is robust with respect to small geometrical deformations of the cavity, while the higher order modes are associated with ray chaos and short-lived. We discuss the incidence of these results on the modification of the spontaneous emission dynamics of an emitter placed in such a parabolic dome microcavity.Comment: 50 pages, 17 figure

Differential influences of early growth and social factors on young children's cognitive performance in four low-and-middle-income birth cohorts (Brazil, Guatemala, Philippines, and South Africa)

Background: Studies relating childhood cognitive development to poor linear growth seldom take adequate account of social conditions related to both, leading to a focus on nutrition interventions. We aimed to assess the roles of both biological and social conditions in determining early childhood cognition, mediated by birthweight and early linear growth. Methods: After exploratory structural equation modelling to identify determining factors, we tested direct and indirect paths to cognitive performance through birthweight and child height-for-age at 2 years, assessed between 4 and 8.5 years of age among 2448 children in four birth cohort studies in low-and-middle-income countries (Brazil, Guatemala, Philippines and South Africa). Determinants were compared across the cohorts. Findings: Three factors yielded excellent fit, comprising birth endowment (primarily maternal age and birth order), household resources (crowding, dependency) and parental capacity (parental education). We estimated their strength together with maternal height in determining cognitive performance. Percentage shares of total effects of the four determinants show a marked transition from mainly biological determinants of birth weight (birth endowment 34%) and maternal height (30%) compared to household resources (25%) and parental capacity (11%), through largely economic determinants of height at 2 years (household resources (60%) to cognitive performance being predominantly determined by parental capacity (64%) followed by household resources (29%). The largely biological factor, birth endowment (maternal age and birth order) contributed only 7% to childhood cognitive performance and maternal height was insignificant. In summary, the combined share of social total effects (household resources and parental capacity) rises from 36∙2% on birth weight, to 78∙2% on height for age at 24 m, and 93∙4% on cognitive functioning. Interpretation: Across four low- and middle-income contexts, cognition in childhood is influenced more by the parental capacity of families and their economic resources than by birth weight and early linear growth. Improving children's cognitive functioning requires multi-sectoral interventions to improve parental education and enhance their economic wellbeing, interventions that are known to improve also early childhood growth

Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review article. This version corrects two further typographic errors (three total with respect to the published version), see page 2 for detail

Angle-integrated measurements of the 26Al (d, n)27Si reaction cross section: a probe of spectroscopic factors and astrophysical resonance strengths

Measurements of angle-integrated cross sections to discrete states in 27Si have been performed studying the 26Al (d, n) reaction in inverse kinematics by tagging states by their characteristic $\gamma$ -decays using the GRETINA array. Transfer reaction theory has been applied to derive spectroscopic factors for strong single-particle states below the proton threshold, and astrophysical resonances in the 26Al (p,$\gamma$) 27Si reaction. Comparisons are made between predictions of the shell model and known characteristics of the resonances. Overall very good agreement is obtained, indicating this method can be used to make estimates of resonance strengths for key reactions currently largely unconstrained by experiment

The MeerKAT Fornax Survey

We present the science case and observations plan of the MeerKAT Fornax Survey, an HI and radio continuum survey of the Fornax galaxy cluster to be carried out with the SKA precursor MeerKAT. Fornax is the second most massive cluster within 20 Mpc and the largest nearby cluster in the southern hemisphere. Its low X-ray luminosity makes it representative of the environment where most galaxies live and where substantial galaxy evolution takes place. Fornax's ongoing growth makes it an excellent laboratory for studying the assembly of clusters, the physics of gas accretion and stripping in galaxies falling in the cluster, and the connection between these processes and the neutral medium in the cosmic web. We will observe a region of 12 deg2 reaching a projected distance of 1.5 Mpc from the cluster centre. This will cover a wide range of environment density out to the outskirts of the cluster, where gas-rich in-falling groups are found. We will: study the HI morphology of resolved galaxies down to a column density of a few times 1e+19 cm−2 at a resolution of 1 kpc; measure the slope of the HI mass function down to M(HI) 5e+5 M(sun); and attempt to detect HI in the cosmic web reaching a column density of 1e+18 cm−2 at a resolution of 10 kpc