Sharp measure contraction property for generalized H-type Carnot groups

We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. This constitutes the largest class of Carnot groups for which the curvature exponent coincides with the geodesic dimension. We stress that generalized H-type Carnot groups have step 2, include all corank 1 groups and, in general, admit abnormal minimizing curves. As a corollary, we prove the absolute continuity of the Wasserstein geodesics for the quadratic cost on all generalized H-type Carnot groups.Comment: 18 pages. This article extends the results of arXiv:1510.05960. v2: revised and improved version. v3: final version, to appear in Commun. Contemp. Mat

Intertwined orders from symmetry projected wavefunctions of repulsively interacting Fermi gases in optical lattices

Unconventional strongly correlated phases of the repulsive Fermi-Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. In a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d-wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting spiral magnetism and evolves towards a doped antiferromagnet. A concomitant enhancement of long-ranged d-wave pairing correlations is also found. Numerical tests of the approach for two-dimensional clusters are carried out, too.Comment: 26 pages, 15 figures ; replaced with the published manuscript ; substantial changes from previous versio

Experimental investigation of the effect of spatial aggregation on reproductive success in a rewardless orchid

Plant reproductive success within a patch may depend on plant aggregation through pollinator attraction. For rewardless plants that lack rewards for pollinators, reproductive success may rely strongly on the learning abilities of pollinators. These abilities depend on relative co-flowering rewarding and rewardless plant species spatial distributions. We investigated the effect of aggregation on the reproductive success of a rewardless orchid by setting up 16 arrays in a factorial design with two levels of intraspecific aggregation for both a rewardless orchid and a rewarding co-flowering species. Our results show that increasing aggregation of both species negatively influenced the reproductive success of the rewardless plants. To our knowledge, this is the first experimental study demonstrating negative effects of aggregation on reproductive success of a rewardless species due both to its own spatial aggregation and that of a co-flowering rewarding species. We argue that pollinator learning behaviour is the key driver behind this result

Do rewardless orchids show a positive relationship between phenotypic diversity and reproductive success?

Among rewardless orchids, pollinator sampling behavior has been suggested to drive a positive relationship between population phenotypic variability and absolute reproductive success, and hence population fitness. We tested this hypothesis by constructing experimental arrays using the rewardless orchid Dactylorhiza sambucina, which is dimorphic for corolla color. We found no evidence that polymorphic arrays had higher mean reproductive success than monomorphic arrays for pollinia removal, pollen deposition, or fruit set. For pollinia removal, monomorphic yellow arrays had significantly greater reproductive success, and monomorphic red the least. A tendency for yellow arrays to have higher pollen deposition was also found. We argue that differential population fitness was most likely to reflect differential numbers of pollinators attracted to arrays, through preferential long-distance attraction to arrays with yellow inflorescences. Correlative studies of absolute reproductive success in 52 populations of D. sambucina supported our experimental results. To our knowledge this is the first study to suggest that attraction of a greater number of pollinators to rewardless orchids may be of greater functional importance to population fitness, and thus ecology and conservation, than are the behavioral sequences of individual pollinators

Pollination of the European food-deceptive Traunsteinera globosa (Orchidaceae): the importance of nectar-producing neighbouring plants

ISSN:0378-2697ISSN:1615-611

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

Effective interaction for pf-shell nuclei

An effective interaction is derived for use in the full pf basis. Starting from a realistic G-matrix interaction, 195 two-body matrix elements and 4 single-particle energies are determined by fitting to 699 energy data in the mass range 47 to 66. The derived interaction successfully describes various structures of pf-shell nuclei. As examples, systematics of the energies of the first 2+ states in the Ca, Ti, Cr, Fe, and Ni isotope chains and energy levels of 56,57,58Ni are presented. The appearance of a new magic number 34 is seen.Comment: 5 pages, 4 figures, to be published in Phys. Rev.

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.

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