Superconducting phase coherence in the presence of a pseudogap: Relation to specific heat, tunneling and vortex core spectroscopies

In this paper we demonstrate how, using a natural generalization of BCS theory, superconducting phase coherence manifests itself in phase insensitive measurements, when there is a smooth evolution of the excitation gap \Delta from above to below Tc. In this context, we address the underdoped cuprates. Our premise is that just as Fermi liquid theory is failing above Tc, BCS theory is failing below. The order parameter \Delta_{sc} is different from the excitation gap \Delta. Equivalently there is a (pseudo)gap in the excitation spectrum above Tc which is also present in the underlying normal state of the superconducting phase, and can be directly inferred from specific heat and vortex core experiments. At the same time many features of BCS theory, e.g., fermionic quasiparticles below Tc, are clearly present. These observations can be reconciled by a natural extension of BCS theory, which includes finite center-of-mass momentum pair excitations, in addition to the usual fermionic quasiparticles. Applying this theory we find that the Bose condensation of Cooper pairs, which is reflected in \Delta_{sc}, leads to sharp peaks in the spectral function once $T \le T_c$. These are manifested in ARPES spectra as well as in specific heat jumps, which become more like the behavior in a \lambda transition as the pseudogap develops. We end with a discussion of tunneling experiments and condensation energy issues. Comparison between theoretical and experimental plots of C_v, and of tunneling and vortex core spectroscopy measurements is good.Comment: 12 pages, 8 figures, ReVTeX 3.

Non-perturbative approach to the attractive Hubbard model

A non-perturbative approach to the single-band attractive Hubbard model is presented in the general context of functional derivative approaches to many-body theories. As in previous work on the repulsive model, the first step is based on a local-field type ansatz, on enforcement of the Pauli principle and a number of crucial sum-rules. The Mermin-Wagner theorem in two dimensions is automatically satisfied. At this level, two-particle self-consistency has been achieved. In the second step of the approximation, an improved expression for the self-energy is obtained by using the results of the first step in an exact expression for the self-energy where the high- and low-frequency behaviors appear separately. The result is a cooperon-like formula. The required vertex corrections are included in this self-energy expression, as required by the absence of a Migdal theorem for this problem. Other approaches to the attractive Hubbard model are critically compared. Physical consequences of the present approach and agreement with Monte Carlo simulations are demonstrated in the accompanying paper (following this one).Comment: Revtex, 19 page

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron

‘Test Driving’ a Financing Instrument for Climate Adaptation: Analyzing Institutional Dilemmas using Simulation Gaming

Urban physical public infrastructure is a frontline defense mechanism to manage and mitigate climate-related impacts. Market instruments are often cited as possible means to spread risk and reduce financial burdens on the public sector. The authors argue that existing research tends to focus on the technical issues of instruments and neglects considering institutional dynamics that may enable or constrain local market-based financing mechanisms. In this article, three core dilemmas (values uncertainty, planning horizon, and indirect benefits) are used to analyze the responses of practitioners to a possible financing instrument. The findings indicate that the practitioner’s responses to tax increment financing were largely shaped by the adaptation dilemmas and not the characteristics of the instrument per se. By mapping the dilemmas onto whether they would recommend it, participants imposed a financial barrier on climate adaptation investments. The authors conclude that a key imperative in the design of policy instruments is to pay attention to the congruency of informal institutions at the ‘street level’ in order to be in-step with the current sociopolitical conditions. The findings also point to four key attributes that a local market-based instrument would need to be aligned and responsive to the Dutch planning and development context

Pairing fluctuations and pseudogaps in the attractive Hubbard model

The two-dimensional attractive Hubbard model is studied in the weak to intermediate coupling regime by employing a non-perturbative approach. It is first shown that this approach is in quantitative agreement with Monte Carlo calculations for both single-particle and two-particle quantities. Both the density of states and the single-particle spectral weight show a pseudogap at the Fermi energy below some characteristic temperature T*, also in good agreement with quantum Monte Carlo calculations. The pseudogap is caused by critical pairing fluctuations in the low-temperature renormalized classical regime $\omega < T$ of the two-dimensional system. With increasing temperature the spectral weight fills in the pseudogap instead of closing it and the pseudogap appears earlier in the density of states than in the spectral function. Small temperature changes around T* can modify the spectral weight over frequency scales much larger than temperature. Several qualitative results for the s-wave case should remain true for d-wave superconductors.Comment: 20 pages, 12 figure

Apprentissage des interdépendances et des dynamiques

National audienc

Rendimento de grãos, componentes do rendimento e índice SPAD do feijoeiro (Phaseolus vulgaris L.) em função de época de aplicação e do parcelamento da aplicação foliar de molibdênio Grain yield, yield components and bean SPAD index of common bean (Phaseolus vulgaris L.) in relation to time and partitioning of molybdenum foliar spray

Objetivando avaliar a influência da época de aplicação e do parcelamento da dose de molibdênio, aplicado via foliar sobre os componentes da produção e índice SPAD do feijoeiro (Phaseolus vulgaris L.), variedade Meia Noite, conduziram-se dois experimentos em área da Universidade Federal de Viçosa, no município de Coimbra, MG, semeados em março e julho de 2002. O delineamento experimental foi o de blocos casualizados, com dez tratamentos e quatro repetições. Os tratamentos avaliados foram: 1- testemunha, sem Mo; 2- 80 g ha-1 de Mo aplicados 15 dias após a emergência (DAE); 3- 40 g ha-1 de Mo aplicados 15 DAE e 40 g ha-1 20 DAE; 4- 40 g ha-1 de Mo 15 DAE e 40 g ha-1 25 DAE; 5- 40 gha-1 de Mo 15 DAE e 40 g ha-1 30 DAE; 6- 80 gha-1 de Mo 20 DAE; 7- 40 g ha-1 de Mo 20 DAE e 40 g ha-1 25 DAE; 8- 40 g ha-1 de Mo 20 DAE e 40 gha-1 30 DAE; 9- 80 g ha-1 de Mo 25 DAE; 10- 40 g ha-1 de Mo 25 DAE e 40 g ha-1 30 DAE. Os dados dos dois experimentos foram submetidos a uma análise conjunta. A adubação foliar molíbdica aumenta a produtividade e o índice SPAD no cultivo de verão-outono com início aos 15 e 20 DAE, mas não aos 25 DAE. O parcelamento da dose não aumenta a produtividade. No cultivo de inverno-primavera, os tratamentos com molibdênio aumentam a produtividade.<br>A field trial was undertaken to evaluate the effect of the foliar application and dose partitioning of molybdenum on yield components and SPAD index of common bean (Phaseolus vulgaris L.), var. Meia Noite, sowed in March and in July of 2002, in an area of the Universidade Federal de Viçosa, Coimbra, MG. The randomized block experimental design was used with ten treatments and four replicates: The appraised treatments were: 1 control, without Mo; 2 - 80 g ha-1 Mo applied at 15 days after emergency (DAE); 3 - 40 g ha-1 Mo applied at 15 DAE, and 40g at 20 DAE; 4 - 40 g ha-1 Mo applied at 15 DAE, and 40 g ha-1 Mo at 25 DAE; 5 - 40 g ha-1 Mo applied at 15 DAE, and 40 g ha-1 Mo at 30 DAE; 6 - 80 g ha-1 Mo applied at 20 DAE; 7 - 40 g ha-1 Mo applied at 20 DAE, and 40 g ha-1 Mo at 25 DAE; 8 - 40 g ha-1 Mo applied at 20 DAE, and 40 g ha-1 Mo at 30 DAE; 9 80 g ha-1 Mo applied at 25 DAE; 10 - 40 g ha-1 Mo applied at 25 DAE, and 40 g ha-1 Mo at 30 DAE. ). Data of two trials were submitted to combined analysis. Molybdenum foliar spray increased yield and SPAD index in summer-autumn cultivation when started 15 or 20 DAE, but not 25 DAE. Dose partitioning had no effect on yield increase yield. In winter-spring cultivation, all molybdenum treatments increased yield