Abrupt sea surface pH change at the end of the Younger Dryas in the central sub-equatorial Pacific inferred from boron isotope abundance in corals (<i>Porites</i>)

The "δ¹¹B-pH" technique was applied to modern and ancient corals <i>Porites</i> from the sub-equatorial Pacific areas (Tahiti and Marquesas) spanning a time interval from 0 to 20.720 calendar years to determine the amplitude of pH changes between the Last Glacial Period and the Holocene. Boron isotopes were measured by Multi-Collector – Inductively Coupled Plasma Mass Spectrometry (MC-ICPMS) with an external reproducibility of 0.25&permil;, allowing a precision of about &plusmn;0.03 pH-units for pH values between 8 and 8.3. The boron concentration [B] and isotopic composition of modern samples indicate that the temperature strongly controls the partition coefficient K_<i>D</i> for different aragonite species. Modern coral δ¹¹B values and the reconstructed sea surface pH values for different Pacific areas match the measured pH expressed on the seawater scale and confirm the calculation parameters that were previously determined by laboratory calibration exercises. Most ancient sea surface pH reconstructions near Marquesas are higher than modern values. These values range between 8.19 and 8.27 for the Holocene and reached 8.30 at the end of the last glacial period (20.7 kyr BP). At the end of the Younger Dryas (11.50&plusmn;0.1 kyr BP), the central sub-equatorial Pacific experienced a dramatic drop of up to 0.2 pH-units from the average pH of 8.2 before and after this short event. Using the marine carbonate algorithms, we recalculated the aqueous <i>p</i>CO₂ to be 440&plusmn;25 ppmV at around 11.5 kyr BP for corals at Marquesas and ~500 ppmV near Tahiti where it was assumed that <i>p</i>CO₂ in the atmosphere was 250 ppmV. Throughout the Holocene, the difference in <i>p</i>CO₂ between the ocean and the atmosphere at Marquesas (Δ<i>p</i>CO₂) indicates that the surface waters behave as a moderate CO₂ sink or source (−53 to 20 ppmV) during El Niño-like conditions. By contrast, during the last glacial/interglacial transition, this area was a marked source of CO₂ (21 to 92 ppmV) for the atmosphere, highlighting predominant La Niña-like conditions. Such conditions were particularly pronounced at the end of the Younger Dryas with a large amount of CO₂ released with Δ<i>p</i>CO₂ of +185&plusmn;25 ppmV. This last finding provides further evidence of the marked changes in the surface water pH and temperature in the equatorial Pacific at the Younger Dryas-Holocene transition and the strong impact of oceanic dynamic on the atmospheric CO₂ content

New Lower Bound on Fermion Binding Energies

We derive a new lower bound for the ground state energy $E^{\rm F}(N,S)$ of N fermions with total spin S in terms of binding energies $E^{\rm F}(N-1,S \pm 1/2)$ of (N-1) fermions. Numerical examples are provided for some simple short-range or confining potentials.Comment: 4 pages, 1 eps figur

Exact quantum jump approach to open systems in Bosonic and spin baths

A general method is developed which enables the exact treatment of the non-Markovian quantum dynamics of open systems through a Monte Carlo simulation technique. The method is based on a stochastic formulation of the von Neumann equation of the composite system and employs a pair of product states following a Markovian random jump process. The performance of the method is illustrated by means of stochastic simulations of the dynamics of open systems interacting with a Bosonic reservoir at zero temperature and with a spin bath in the strong coupling regime.Comment: 4 pages, 2 figure

Neel Order and Electron Spectral Functions in the Two-Dimensional Hubbard Model: a Spin-Charge Rotating Frame Approach

Using recently developed quantum SU(2)xU(1) rotor approach, that provides a self-consistent treatment of the antiferromagnetic state we have performed electronic spectral function calculations for the Hubbard model on the square lattice. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green's function in the space-time domain as the product CP^1 propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. As a result the problem of calculating the spectral line shapes now becomes one of performing the convolution of spin, charge and pseudo-fermion Green's functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.Comment: 16 pages, 5 figures, submitted to Phys. Rev.

Local Density Approximation for proton-neutron pairing correlations. I. Formalism

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.Comment: 22 RevTeX page

An exact stochastic mean-field approach to the fermionic many-body problem

We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of Time Dependent Hartree-Fock equations. The noise is found from a path-integral representation of the evolution operator and allows to interpret the exact N-body state as a coherent average over Slater determinants evolving under the random mean-fied. The full density operator and the expectation value of any observable are then reconstructed using pairs of stochastic uncorrelated wave functions. The imaginary time propagation is also presented and gives a similar stochastic one-body scheme which converges to the exact ground state without developing a sign problem. In addition, the growth of statistical errors is examined to show that the stochastic formulation never explode in a finite dimensional one-body space. Finally, we consider initially correlated systems and present some numerical implementations in exactly soluble models to analyse the precision and the stability of the approach in practical cases

Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry

We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry

Madagascar corals track sea surface temperature variability in the Agulhas Current core region over the past 334 years

The Agulhas Current (AC) is the strongest western boundary current in the Southern Hemisphere and is key for weather and climate patterns, both regionally and globally. Its heat transfer into both the midlatitude South Indian Ocean and South Atlantic is of global significance. A new composite coral record (Ifaty and Tulear massive Porites corals), is linked to historical AC sea surface temperature (SST) instrumental data, showing robust correlations. The composite coral SST data start in 1660 and comprise 200 years more than the AC instrumental record. Numerical modelling exhibits that this new coral derived SST record is representative for the wider core region of the AC. AC SSTs variabilities show distinct cooling through the Little Ice Age and warming during the late 18th, 19th and 20th century, with significant decadal variability superimposed. Furthermore, the AC SSTs are teleconnected with the broad southern Indian and Atlantic Oceans, showing that the AC system is pivotal for inter-ocean heat exchange south of Africa

A user's guide to optimal transport

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below