The effect of colored noise on heteroclinic orbits

The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of the system, is derived analytically in the case where noise is an additive Kubo-Anderson process. This theory shows how the geometry of the separatrix, as well as the noise intensity and correlation time, affect the statistics of crossing. Results can be applied to a wide variety of systems, and are valid in the limit where the noise correlation time scale is much smaller than the time scale of the undisturbed Hamiltonian dynamics

Effect of nonuniform hole-content distribution within the interlayer pair-tunneling mechanism of layered HTSC

The interlayer pair-tunneling (ILT) mechanism for high-$T_c$ superconductivity is able to predict the dependence of the (optimal) critical temperature Tc on the number of layers n within an homologous series of layered cuprate oxides. We generalize the mean-field procedure employed to evaluate Tc within an extended in-plane Hubbard model in presence of ILT, developed for a bilayer complex (n = 2), to the case of n = 3, 4 inequivalent superconducting layers. As a function of doping, we show how a nonuniform hole-content distribution among different layers affects Tc. In particular, depending on doping, the onset of superconductivity may be ruled by inner or outer layers. The latter result may be related to recent experimental data of Tc as a function of pressure in Tl- and Bi-based layered superconductors

Pressure-induced electronic topological transitions in low dimensional superconductors

In the high-Tc cuprates, the unusual dependence of Tc on external pressure results from the combination of the nonmonotonic dependence of Tc on hole doping or hole-doping distribution among inequivalent layers, and from an ``intrinsic'' contribution. After reviewing our work on the interplay among Tc, hole content, and pressure in the bilayered and multilayered cuprate superconductors, we will discuss how the proximity to an electronic topological transition (ETT) may give a microscopic justification of the ``intrinsic'' pressure dependence of Tc in the cuprates. As a function of the proximity to an ETT, we recover a nonmonotonic behaviour of the superconducting gap at T=0, regardless of the pairing symmetry of the order parameter. This is in agreement with the trend observed for Tc as a function of pressure and other material specific quantities in several high-Tc cuprates. In the case of epitaxially strained cuprate thin films, we argue that an ETT can be driven by a strain-induced modification of the in-plane band structure, at constant hole content, at variance with a doping-induced ETT, as is usually assumed. We also find that an increase of the in-plane anisotropy enhances the effect of fluctuations above Tc on the normal-state transport properties, which is a fingerprint of quantum criticality at T=0.Comment: EHPRG Award Lecture, http://www.ehprg.org. To be published in J. Phys.: Cond. Matte

Critical Stokes number for the capture of inertial particles by recirculation cells in 2D quasi-steady flows

Inertial particles are often observed to be trapped, temporarily or permanently, by recirculation cells which are ubiquitous in natural or industrial flows. In the limit of small particle inertia, determining the conditions of trapping is a challenging task, as it requires a large number of numerical simulations or experiments to test various particle sizes or densities. Here, we investigate this phenomenon analytically and numerically in the case of heavy particles (e.g. aerosols) at low Reynolds number, to derive a trapping criterion that can be used both in analytical and numerical velocity fields. The resulting criterion allows to predict the characteristics of trapped particles as soon as single-phase simulations of the flow are performed. Our analysis is valid for two-dimensional particle-laden flows in the vertical plane, in the limit where the particle inertia, the free-fall terminal velocity, and the flow unsteadiness can be treated as perturbations. The weak unsteadiness of the flow generally induces a chaotic tangle near heteroclinic or homoclinic cycles if any, leading to the apparent diffusion of fluid elements through the boundary of the cell. The critical particle Stokes number Stc below which aerosols also enter and exit the cell in a complex manner has been derived analytically, in terms of the flow characteristics. It involves the non-dimensional curvature-weighted integral of the squared velocity of the steady fluid flow along the dividing streamline of the recirculation cell. When the flow is unsteady and St > Stc, a regular motion takes place due to gravity and centrifugal effects, like in the steady case. Particles driven towards the interior of the cell are trapped permanently. In contrast, when the flow is unsteady and St < Stc, particles wander in a chaotic manner in the vicinity of the border of the cell, and can escape the cell

Note on dust trapping in inviscid vortex pairs with unequal strengths

We investigate theoretically the motion of tiny heavy passive particles transported in a plane inviscid flow consisting of two point vortices, in order to understand particle dispersion and trapping during vortex interaction. In spite of their large density, particles are not necessarily centrifugated away from vortices. It is observed that they can have various equilibrium positions in the reference frame rotating with the vortices, provided the particle response time and the vortex strength ratio lie in appropriate ranges. A stability analysis reveals that some of these points can be asymptotically stable, and can therefore trap particles released in their basin of attraction. A complete trapping diagram is derived, showing that any vortex pair can potentially become a dust trap, provided the vortex strength ratio is different from 0 (single vortex) and -1 (translating symmetrical vortices). Trapping exists for both co-rotating or contra-rotating vortex pairs. In the latter case, particle trapping on a limit cycle is also observed, and confirmed by using Sapsis and Haller's method [Chaos, 20, 017515, 2010] generalized to non-inertial reference frames

Multiband superconductors close to a 3D-2D electronic topological transition

Within the two-band model of superconductivity, we study the dependence of the critical temperature Tc and of the isotope exponent alpha in the proximity to an electronic topological transition (ETT). The ETT is associated with a 3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband of the diborides. Our results agree with the observed dependence of Tc on Mg content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be interpreted as due to the proximity to a "shape resonance". Moreover we have calculated a possible variation of the isotope effect on the superconducting critical temperature by tuning the chemical potential.Comment: J. Supercond., to appea