Correlated percolation models of structured habitat in ecology

Percolation offers acknowledged models of random media when the relevant medium characteristics can be described as a binary feature. However, when considering habitat modeling in ecology, a natural constraint comes from nearest-neighbor correlations between the suitable/unsuitable states of the spatial units forming the habitat. Such constraints are also relevant in the physics of aggregation where underlying processes may lead to a form of correlated percolation. However, in ecology, the processes leading to habitat correlations are in general not known or very complex. As proposed by Hiebeler [Ecology {\bf 81}, 1629 (2000)], these correlations can be captured in a lattice model by an observable aggregation parameter $q$, supplementing the density $p$ of suitable sites. We investigate this model as an instance of correlated percolation. We analyze the phase diagram of the percolation transition and compute the cluster size distribution, the pair-connectedness function $C(r)$ and the correlation function $g(r)$. We find that while $g(r)$ displays a power-law decrease associated with long-range correlations in a wide domain of parameter values, critical properties are compatible with the universality class of uncorrelated percolation. We contrast the correlation structures obtained respectively for the correlated percolation model and for the Ising model, and show that the diversity of habitat configurations generated by the Hiebeler model is richer than the archetypal Ising model. We also find that emergent structural properties are peculiar to the implemented algorithm, leading to questioning the notion of a well-defined model of aggregated habitat. We conclude that the choice of model and algorithm have strong consequences on what insights ecological studies can get using such models of species habitat

Critical Opalescence in Baryonic QCD Matter

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behaviour is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.Comment: 7 pages, 1 figur

Quantifying the tangling of trajectories using the topological entropy

We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or three-dimensional magnetic fields, which are periodic in one direction. This method is based on measuring the length of a material line in the flow. Depending on the nature of the flow, the fluid can be mixed very efficiently which causes the line to stretch. Here we study a method that adaptively increases the resolution at locations along the line where folds lead to high curvature. This reduces the computational cost greatly which allows us to study unprecedented parameter regimes. We demonstrate how this efficient implementation allows the computation of the variation of the finite-time topological entropy in the mapping. This measure quantifies spatial variations of the braiding efficiency, important in many practical applications.Comment: 11 pages, 9 figure

Quantized conductance in a one-dimensional ballistic oxide nanodevice

Electric-field effect control of two-dimensional electron gases (2-DEG) has enabled the exploration of nanoscale electron quantum transport in semiconductors. Beyond these classical materials, transition metal-oxide-based structures have d-electronic states favoring the emergence of novel quantum orders absent in conventional semiconductors. In this context, the LaAlO3/SrTiO3 interface that combines gate-tunable superconductivity and sizeable spin-orbit coupling is emerging as a promising platform to realize topological superconductivity. However, the fabrication of nanodevices in which the electronic properties of this oxide interface can be controlled at the nanoscale by field-effect remains a scientific and technological challenge. Here, we demonstrate the quantization of conductance in a ballistic quantum point contact (QPC), formed by electrostatic confinement of the LaAlO3/SrTiO3 2-DEG with a split-gate. Through finite source-drain voltage, we perform a comprehensive spectroscopic investigation of the 3d energy levels inside the QPC, which can be regarded as a spectrometer able to probe Majorana states in an oxide 2-DEG

Competition between electron pairing and phase coherence in superconducting interfaces

In LaAlO3/SrTiO3 heterostructures, a gate tunable superconducting electron gas is confined in a quantum well at the interface between two insulating oxides. Remarkably, the gas coexists with both magnetism and strong Rashba spin–orbit coupling. However, both the origin of superconductivity and the nature of the transition to the normal state over the whole doping range remain elusive. Here we use resonant microwave transport to extract the superfluid stiffness and the superconducting gap energy of the LaAlO3/SrTiO3 interface as a function of carrier density. We show that the superconducting phase diagram of this system is controlled by the competition between electron pairing and phase coherence. The analysis of the superfluid density reveals that only a very small fraction of the electrons condenses into the superconducting state. We propose that this corresponds to the weak filling of high- energy dxz/dyz bands in the quantum well, more apt to host superconductivity

Field-effect control of superconductivity and Rashba spin-orbit coupling in top-gated LaAlO3/SrTiO3 devices

The recent development in the fabrication of artificial oxide heterostructures opens new avenues in the field of quantum materials by enabling the manipulation of the charge, spin and orbital degrees of freedom. In this context, the discovery of two-dimensional electron gases (2-DEGs) at LAlO3/SrTiO3 interfaces, which exhibit both superconductivity and strong Rashba spin-orbit coupling (SOC), represents a major breakthrough. Here, we report on the realisation of a field-effect LaAlO3/SrTiO3 device, whose physical properties, including superconductivity and SOC, can be tuned over a wide range by a top-gate voltage. We derive a phase diagram, which emphasises a field-effect-induced superconductor-to-insulator quantum phase transition. Magneto-transport measurements indicate that the Rashba coupling constant increases linearly with electrostatic doping. Our results pave the way for the realisation of mesoscopic devices, where these two properties can be manipulated on a local scale by means of top-gates

Constructing and exploring wells of energy landscapes

Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic explorations of the relief and introduce as basic topographic features ``wells of duration $T$ and altitude $y$''. We determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time, whose finite-difference approximations on finite grids yield a constructive algorithm for determining the wells. Our main results are thus (i) a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape, (ii) an alternative to stochastic gradient dynamics for performing such an exploration, (iii) a constructive access to the wells and (iv) the determination of some bare dynamic features inherent to the landscape. The mathematical tools used here are not familiar in physics: They come from set-valued analysis (differential calculus of set-valued maps and differential inclusions) and viability theory (capture basins of targets under evolutionary systems) which have been developed during the last two decades; we therefore propose a minimal appendix exposing them at the end of this paper to bridge the possible gap.Comment: 28 pages, submitted to J. Math. Phys -