Remarks on the naturality of quantization

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's constant, the Hilbert spaces of the quantization form a bundle over U with a natural connection. In this paper we examine the dependence of the Hilbert spaces on the choice of J, by computing the semi-classical limit of the curvature of this connection. We also show that parallel transport provides a link between the action of the group Symp(M) of symplectomorphisms of M and the Schrodinger equation.Comment: 20 page

Two-phase densification of cohesive granular aggregates

When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressed upon with a ram, these aggregates densify by particle rearrangement. Here we introduce experimental evidence to the effect that particle rearrangement is a spatially heterogeneous phenomenon, which occurs in the form of a phase transformation between two configurational phases of the granular aggregate. We then show that the energy landscape associated with particle rearrangement is consistent with our interpretation of the experimental results. Besides affording insight into the physics of the granular state, our conclusions are relevant to many engineering processes and natural phenomena.Comment: 7 pages, 3 figure

Evidence for spin-triplet superconducting correlations in metal-oxide heterostructures with non-collinear magnetization

Heterostructures composed of ferromagnetic La0.7Sr0.3MnO3, ferromagnetic SrRuO3, and superconducting YBa2Cu3Ox were studied experimentally. Structures of composition Au/La0.7Sr0.3MnO3/SrRuO3/YBa2Cu3Ox were prepared by pulsed laser deposition, and their high quality was confirmed by X-ray diffraction and reflectometry. A non-collinear magnetic state of the heterostructures was revealed by means of SQUID magnetometry and polarized neutron reflectometry. We have further observed superconducting currents in mesa-structures fabricated by deposition of a second superconducting Nb layer on top of the heterostructure, followed by patterning with photolithography and ion-beam etching. Josephson effects observed in these mesa-structures can be explained by the penetration of a triplet component of the superconducting order parameter into the magnetic layers.Comment: 10 pages, 6 figure

Depth profile of the ferromagnetic order in a YBa2_2Cu3_3O7_7 / La2/3_{2/3}Ca1/3_{1/3}MnO3_3 superlattice on a LSAT substrate: a polarized neutron reflectometry study

Using polarized neutron reflectometry (PNR) we have investigated a YBa2Cu3O7(10nm)/La2/3Ca1/3MnO3(9nm)]10 (YBCO/LCMO) superlattice grown by pulsed laser deposition on a La0.3Sr0.7Al0.65Ta0.35O3 (LSAT) substrate. Due to the high structural quality of the superlattice and the substrate, the specular reflectivity signal extends with a high signal-to-background ratio beyond the fourth order superlattice Bragg peak. This allows us to obtain more detailed and reliable information about the magnetic depth profile than in previous PNR studies on similar superlattices that were partially impeded by problems related to the low temperature structural transitions of the SrTiO3 substrates. In agreement with the previous reports, our PNR data reveal a strong magnetic proximity effect showing that the depth profile of the magnetic potential differs significantly from the one of the nuclear potential that is given by the YBCO and LCMO layer thickness. We present fits of the PNR data using different simple block-like models for which either a ferromagnetic moment is induced on the YBCO side of the interfaces or the ferromagnetic order is suppressed on the LCMO side. We show that a good agreement with the PNR data and with the average magnetization as obtained from dc magnetization data can only be obtained with the latter model where a so-called depleted layer with a strongly suppressed ferromagnetic moment develops on the LCMO side of the interfaces. The models with an induced ferromagnetic moment on the YBCO side fail to reproduce the details of the higher order superlattice Bragg peaks and yield a wrong magnitude of the average magnetization. We also show that the PNR data are still consistent with the small, ferromagnetic Cu moment of 0.25muB that was previously identified with x-ray magnetic circular dichroism and x-ray resonant magnetic reflectometry measurements on the same superlattice.Comment: 11 pages, 7 figure

Legendrian Distributions with Applications to Poincar\'e Series

Let $X$ be a compact Kahler manifold and $L\to X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $\Lambda$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences $\{ |\Lambda, k\rangle \}_{k=1}^\infty$, where $\forall k$ $|\Lambda, k\rangle$ is a holomorphic section of $L^{\otimes k}$. The terms in each sequence concentrate on $\Lambda$, and a sequence itself has a symbol which is a half-form, $\sigma$, on $\Lambda$. We prove estimates, as $k\to\infty$, of the norm squares $\langle \Lambda, k|\Lambda, k\rangle$ in terms of $\int_\Lambda \sigma\overline{\sigma}$. More generally, we show that if $\Lambda_1$ and $\Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $\langle\Lambda_1, k|\Lambda_2, k\rangle$ have an asymptotic expansion as $k\to\infty$, the leading coefficient being an integral over the intersection $\Lambda_1\cap\Lambda_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincar\'e series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.Comment: 41 pages, LaTe

A Century of Change towards Prevention and Minimal Intervention in Cariology

Publisher Copyright: © International & American Associations for Dental Research 2019. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.Better understanding of dental caries and other oral conditions has guided new strategies to prevent disease and manage its consequences at individual and public health levels. This article discusses advances in prevention and minimal intervention dentistry over the last century by focusing on some milestones within scientific, clinical, and public health arenas, mainly in cariology but also beyond, highlighting current understanding and evidence with future prospects. Dentistry was initially established as a surgical specialty. Dental caries (similar to periodontitis) was considered to be an infectious disease 100 years ago. Its ubiquitous presence and rampant nature—coupled with limited diagnostic tools and therapeutic treatment options—meant that these dental diseases were managed mainly by excising affected tissue. The understanding of the diseases and a change in their prevalence, extent, and severity, with evolutions in operative techniques, technologies, and materials, have enabled a shift from surgical to preventive and minimal intervention dentistry approaches. Future challenges to embrace include continuing the dental profession’s move toward a more patient-centered, evidence-based, less invasive management of these diseases, focused on promoting and maintaining oral health in partnership with patients. In parallel, public health needs to continue to, for example, tackle social inequalities in dental health, develop better preventive and management options for existing disease risk groups (e.g., the growing aging population), and the development of reimbursement and health outcome models that facilitate implementation of these evolving strategies. A century ago, almost every treatment involved injections, a drill or scalpel, or a pair of forceps. Today, dentists have more options than ever before available to them. These are supported by evidence, have a minimal intervention focus, and result in better outcomes for patients. The profession’s greatest challenge is moving this evidence into practice.preprintPeer reviewe

Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree zero, extended Gromov-Witten invariants of the n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As we do not specialize the values of the quantum parameters involved, this result proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of reconstructing the cup product for Hilb^n(S) from the orbifold invariants of [Sym^n(S)].Comment: Revised versio

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog