Electronic structure of C60 / graphite

We report temperature-dependent photoelectron spectra for a monolayer of C_60 adsorbed on HOPG, as well as C 1s x-ray absorption. This extends a previous report which showed the close similarity between the spectrum of the HOMO for the two-dimensional overlayer and that of C_60 in the gas phase. The present work shows that intermolecular and molecule-substrate vibrations contribute strongly to the spectral lineshape at room temperature. Thus, vibrational effects are shown to be crucial for the proper understanding of photoelectron spectra, and thus the charge transport properties, for C_60 in contact with graphite and graphite-like materials.Comment: Proc. of the XV. Int. Winterschool on Electronic Properties of Novel Materials, Kirchberg/Tirol, Austria, 200

Renormalon disappearance in Borel sum of the 1/N expansion of the Gross-Neveu model mass gap

The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally similar to the QCD heavy quark pole mass renormalons, potentially leading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine the precise vanishing mechanism of such infrared renormalons, which avoids this (only apparent)contradiction, and operates without need of (Borel) summation contour prescription, usually preventing unambiguous separation of perturbative contributions. As a consequence we stress the direct Borel summability of the (1/N) perturbative expansion of the mass gap. We briefly speculate on a possible similar behaviour of analogous non-perturbative QCD quantities.Comment: 16 pp., 1 figure. v2: a few paragraphs and one appendix added, title and abstract slightly changed, essential results unchange

Optimized Perturbation Theory for Wave Functions of Quantum Systems

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings.Comment: 11 pages, RevTeX, three ps figure

Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter d. We get a non-perturbative mass gap as the solution of $\hat{J}=0$. In one loop we find that any physical choice for d gives good results for high values of N. In two loops we can determine d self-consistently by the principle of minimal sensitivity and find remarkably accurate results for N>2.Comment: 13 pages, 3 figures, added referenc

The carbon cycle in Mexico: past, present and future of C stocks and fluxes

PublishedThe Supplement related to this article is available online at doi:10.5194/bg-13-223-2016-supplement.We modeled the carbon (C) cycle in Mexico with a process-based approach. We used different available products (satellite data, field measurements, models and flux towers) to estimate C stocks and fluxes in the country at three different time frames: present (defined as the period 2000–2005), the past century (1901–2000) and the remainder of this century (2010–2100). Our estimate of the gross primary productivity (GPP) for the country was 2137 ± 1023 TgC yr−1 and a total C stock of 34 506 ± 7483 TgC, with 20 347 ± 4622 TgC in vegetation and 14 159 ± 3861 in the soil. Contrary to other current estimates for recent decades, our results showed that Mexico was a C sink over the period 1990–2009 (+31 TgC yr−1) and that C accumulation over the last century amounted to 1210 ± 1040 TgC. We attributed this sink to the CO2 fertilization effect on GPP, which led to an increase of 3408 ± 1060 TgC, while both climate and land use reduced the country C stocks by −458 ± 1001 and −1740 ± 878 TgC, respectively. Under different future scenarios, the C sink will likely continue over the 21st century, with decreasing C uptake as the climate forcing becomes more extreme. Our work provides valuable insights on relevant driving processes of the C cycle such as the role of drought in drylands (e.g., grasslands and shrublands) and the impact of climate change on the mean residence time of soil C in tropical ecosystems.The lead author (G. Murray-Tortarolo) thanks CONACYT-CECTI, the University of Exeter and Secretaría de Educación Pública (SEP) for their funding of this project. The authors extend their thanks to Carlos Ortiz Solorio and to the Colegio de Posgraduados for the field soil data and to the Alianza Redd+ Mexico for the field biomass data. This project would not have been possible without the valuable data from the CMIP5 models. A. Arneth, G. Murray-Tortarolo, A. Wiltshire and S. Sitch acknowledge the support of the European Commission-funded project LULCC4C (grant no. 603542). A. Wiltshire was partsupported by the Joint UK DECC/Defra Met Office Hadley Centre Climate Programme (GA01101)

The mass gap and vacuum energy of the Gross-Neveu model via the 2PPI expansion

We introduce the 2PPI (2-point-particle-irreducible) expansion, which sums bubble graphs to all orders. We prove the renormalizibility of this summation. We use it on the Gross-Neveu model to calculate the mass gap and vacuum energy. After an optimization of the expansion, the final results are qualitatively good.Comment: 14 pages,19 eps figures, revtex

A new method for the solution of the Schrodinger equation

We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.Comment: 4 pages, 4 figures, RevTex

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear \delta expansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002

A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures

The optimized linear $\delta$-expansion is applied to multi-field $O(N_1) \times O(N_2)$ scalar theories at high temperatures. Using the imaginary time formalism the thermal masses are evaluated perturbatively up to order $\delta^2$ which considers consistently all two-loop contributions. A variational procedure associated with the method generates nonperturbative results which are used to search for parameters values for inverse symmetry breaking (or symmetry nonrestoration) at high temperatures. Our results are compared with the ones obtained by the one-loop perturbative approximation, the gap equation solutions and the renormalization group approach, showing good agreement with the latter method. Apart from strongly supporting inverse symmetry breaking (or symmetry nonrestoration), our results reveal the possibility of other high temperature symmetry breaking patterns for which the last term in the breaking sequence is $O(N_1-1) \times O(N_2-1)$.Comment: 28 pages,5 eps figures (uses epsf), RevTeX. Only a small misprint in Eq. (2.10) and a couple of typos fixe

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure