On the total curvature and extrinsic area growth of surfaces with tamed second fundamental form

In this paper we show that a complete and non-compact surface immersed in the Euclidean space with quadratic extrinsic area growth has finite total curvature provided the surface has tamed second fundamental form and admits total curvature. In such a case we obtain as well a generalized Chern-Osserman inequality. In the particular case of a surface of nonnegative curvature, we prove that the surface is diffeomorphic to the Euclidean plane if the surface has tamed second fundamental form, and that the surface is isometric to the Euclidean plane if the surface has strongly tamed second fundamental form. In the last part of the paper we characterize the fundamental tone of any submanifold of tamed second fundamental form immersed in an ambient space with a pole and quadratic decay of the radial sectional curvatures.Comment: 19 pages. Title changed and several improvement of the main theorems are done. arXiv admin note: text overlap with arXiv:0805.0323 by other author

Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians

A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length $N$ of the chain, while general states require a bond dimension scaling exponentially. We show that the bond dimension of these MPS approximations can be improved to a constant, independent of the chain length, if we relax our notion of approximation to be more local: for all length-$k$ segments of the chain, the reduced density matrices of our approximations are $\epsilon$-close to those of the exact state. If the state is a ground state of a gapped local Hamiltonian, the bond dimension of the approximation scales like $(k/\epsilon)^{1+o(1)}$, and at the expense of worse but still $\text{poly}(k,1/\epsilon)$ scaling of the bond dimension, we give an alternate construction with the additional features that it can be generated by a constant-depth quantum circuit with nearest-neighbor gates, and that it applies generally for any state with exponentially decaying correlations. For a completely general state, we give an approximation with bond dimension $\exp(O(k/\epsilon))$, which is exponentially worse, but still independent of $N$. Then, we consider the prospect of designing an algorithm to find a local approximation for ground states of gapped local 1D Hamiltonians. When the Hamiltonian is translationally invariant, we show that the ability to find $O(1)$-accurate local approximations to the ground state in $T(N)$ time implies the ability to estimate the ground state energy to $O(1)$ precision in $O(T(N)\log(N))$ time.Comment: 24 pages, 3 figures. v2: Theorem 1 extended to include construction for general states; Lemma 7 & Theorem 2 slightly improved; figures added; lemmas rearranged for clarity; typos fixed. v3: Reformatted & additional references inserte

Effects of rotation in the energy spectrum of C60C_{60}

In this paper, motivated by the experimental evidence of rapidly rotating $C_{60}$ molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static $C_{60}$ are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field

Creating markets for habitat conservation when habitats are heterogeneous

A tradable development rights (TDR) program focusing on biodiversity conservation faces a crucial problem defining which areas of habitat should be considered equivalent. Restricting the trading domain to a narrow area could boost the range of biodiversity conserved but could increase the opportunity cost of conservation. The issue is relevant to Brazil, where TDR-like programs are emerging. Current regulations require each rural property to maintain a forest reserve of at least 20 percent, but nascent policies allow some tradability of this obligation. The authors use a simple, spatially explicit model to simulate a hypothetical state-level program. They find that wider trading domains drastically reduce landholder costs of complying with this regulation and result in environmentally preferable landscapes.Wetlands,Environmental Economics&Policies,Banks&Banking Reform,Water Conservation,Climate Change,Forestry,Environmental Economics&Policies,Wetlands,Climate Change,Banks&Banking Reform

Three-dimensional color code thresholds via statistical-mechanical mapping

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code on the body-centererd cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D string-like and 2D sheet-like logical operators to be $p^{(1)}_\mathrm{3DCC} \simeq 1.9\%$ and $p^{(2)}_\mathrm{3DCC} \simeq 27.6\%$. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the 4- and 6-body random coupling Ising models.Comment: 4+7 pages, 6 figures, 1 tabl

Comparison between Airborne Pollen and Aeroallergen Quantification with the ChemVol Impact Sampler. Olive pollen vs Ole e 1

Comparison between Airborne Pollen and Aeroallergen Quantification with the ChemVol Impact Sampler. Olive pollen vs Ole e 1. Torres M.C.1, C. Antunes2, M.J. Velasco1, R. Ferro2, H. García-Mozo1, R. Ribeiro2, R.Brandao3, Galán, C1 and the HIALINE team4 1Department of Botany, Ecology and Plant Physiology, University of Córdoba 2Department of Chemistry, University of Évora, Portugal 3Department of Biology, University of Évora, Portugal 4J.T.M. Buters, Germany, M. Thibaudon, France, M. Smith, Great Britain, C. Galan, Spain, R. Brandao and C. Antunes, Portugal, G. Reese, Germany, R. Albertini, Italy, L. Grewling, Poland, A. Rantio-Lehtimäki, Finland, S. Jäger and U. Berger, Austria, I. Sauliene, Lithuania, L. Cecchi, Italy Nowadays, pollinosis is affecting a large percentage of population in the countries with a western life style. The existence of allergenic activity in the atmosphere is not only associated to pollen grains and fungal spores, but also to submicronic and paucimicronic biological particles. The origin of these allergens can be due to the rupture of pollen transported in the atmosphere or to the presence of allergens from other parts of the plant making amorphous material with an allergen load. Olive pollen is recognized as one of the main causes of allergic disease in the Mediterranean area. In this study we have tried to compare olive pollen count in the air and Ole e 1 as major allergen of this species, at two different localities in South of Europe: Evora (Portugal) and Córdoba (Spain). At each location both samplers were placed side-by-side. Pollen grains have been sampled using a volumetric Hirst type spore trap. Chemvol high-volume cascade impactor equipped with stages PM>10µm, 10 µm>PM>2.5µm were used for detecting aeroallergens. Ole e 1 major allergen was determined using allergen specific ELISA´s. Similar behaviour between pollen and the total allergenic load was observed during the pollen season. Nevertheless, at some occasions, during the previous and later period of the pollen season, airborne allergenic load was detected in South Spain, due to the contributions from other Oleaceae species. For this reason the use of these two different methodologies allow a better understanding of the allergenic load in the atmosphere. This work was supported in part by the European Agency for Health and Consumers EAHC, Luxembourg, under the grant agreement 20081107

Evidence for entanglement at high temperatures in an engineered molecular magnet

The molecular compound [Fe$_{2}$($\mu_{2}$-oxo)(C$_{3}$H$_{4}$N$_{2}$)$_{6}$(C$_{2}$O$_{4}$)$_{2}$] was designed and synthesized for the first time and its structure was determined using single-crystal X-ray diffraction. The magnetic susceptibility of this compound was measured from 2 to 300 K. The analysis of the susceptibility data using protocols developed for other spin singlet ground-state systems indicates that the quantum entanglement would remain at temperatures up to 732 K, significantly above the highest entanglement temperature reported to date. The large gap between the ground state and the first-excited state (282 K) suggests that the spin system may be somewhat immune to decohering mechanisms. Our measurements strongly suggest that molecular magnets are promising candidate platforms for quantum information processing