Magnetic quantum phase transitions of the antiferromagnetic J_{1}-J_{2} Heisenberg model

We obtain the complete phase diagram of the antiferromagnetic $J_{1}$-$J_{2}$ model, $0\leq \alpha = J_2/J1 \leq 1$, within the framework of the $O(N)$ nonlinear sigma model. We find two magnetically ordered phases, one with N\' eel order, for $\alpha \leq 0.4$, and another with collinear order, for $\alpha\geq 0.6$, separated by a nonmagnetic region, for $0.4\leq \alpha \leq 0.6$, where a gapped spin liquid is found. The transition at $\alpha=0.4$ is of the second order while the one at $\alpha=0.6$ is of the first order and the spin gaps cross at $\alpha=0.5$. Our results are exact at $N\rightarrow\infty$ and agree with numerical results from different methods.Comment: 4 pages, 5 figure

Kondo Quantum Criticality of Magnetic Adatoms in Graphene

We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as $T_{K}\propto|J-J_{c}|^{1/3}$ near the critical coupling $J_{c}$, and the local spin is effectively screened by a \emph{super-ohmic} bath. For this class, the RKKY interaction decays spatially with a fast power law $\sim1/R^{7}$. Away from half filling, we show that the exchange coupling in graphene can be controlled across the quantum critical region by gating. We propose that the vicinity of the Kondo quantum critical point can be directly accessed with scanning tunneling probes and gating.Comment: 4.1 pages, 3 figures. Added erratum correcting exponent nu=1/3. All the other results remain vali

Diferentes enfoques teóricos de investigaçao sobre o ensino e aprendizagem da demonstraçao em geometria

Neste texto, pretendo estabelecer ligações entre a perspectiva apresentada por Harel e Sowder (2007) e outras perspectivas teóricas de investigação, ligadas ao ensino e aprendizagem da demonstração em geometria. Especificamente, com a perpectiva apresentada no artigo “proofs as bears of mathematical knowledge” (Hanna e Barbeau, 2008) e com a perspective ontosemiótica em educação matemática (Godino et al., 2007) na qual está focada a minha própria investigação. Harel e Sowder (2007) estabeleceram um grupo de questões relativas a vários factores: Factores de natureza histórica, epistemológica e matemática; factores de natureza cognitica e, factores de natureza educacional e sócio-culturais. Estabeleceram questões fundamentais, como por exemplo: O que é demonstrar?Porquê ensinar a demonstrar?(...)(p. 806). O significado destas questões será discutido segundo os enfoques teóricos acima referidos

Abordagens moleculares no estudo da diversidade microbiana

A importância dos microrganismos na manutenção da vida na Terra é reconhecida por todos. Estes organismos microscópicos são relevantes em áreas tão diversas como a Saúde, Agricultura, Indústria ou Ambiente. O número estimado de todas as espécies é de 100 milhões, das quais 2 milhões foram formalmente descritas. Das cerca de 1,5 a 3,5 milhões de espécies fúngicas que se estimam existir, apenas 5% se encontram descritas. Tradicionalmente, a identificação de espécies de fungos baseia-se no seu isolamento e análise da morfologia das suas estruturas reprodutoras. Embora de grande utilidade, a caracterização morfológica é limitada devido ao reduzido número de caracteres que podem ser analisados, da dependência das condições de cultura e das variações intrínsecas do microrganismo. Actualmente, métodos moleculares baseados na sequenciação do espaçador interno do transcrito de rDNA (ITS) têm vindo a ser utilizados na identificação eficaz de espécies fúngicas. Estudos populacionais têm recorrido à amplificação da região ITS e comparação dos perfis electroforéticos em gradientes desnaturantes (DGGE ou TGGE) de diferentes amostras. Recentemente, o desenvolvimento de técnicas de sequenciação massiva permitiram a emergência de uma nova área- a metagenómica - que pode ser aplicada a comunidades de microrganismos sem a necessidade de os isolar ou cultivar. Este facto adquire especial relevância por se estimar que apenas 17% dos fungos serão capazes de ser cultivados in vitro. Nesta apresentação serão abordados as estratégias que permitiram a evolução da metagenómica. Os desafios da identificação de microrganismos em comunidades serão discutidos, focando o caso particular da diversidade fúngica em amostras de solos.Financiado pela FCT, projecto PTDC/AGR-AAM/099556/200

The Wheeler-DeWitt Quantization Can Solve the Singularity Problem

We study the Wheeler-DeWitt quantum cosmology of a spatially flat Friedmann cosmological model with a massless free scalar field. We compare the consistent histories approach with the de Broglie-Bohm theory when applied to this simple model under two different quantization schemes: the Schr\"odinger-like quantization, which essentially takes the square-root of the resulting Klein-Gordon equation through the restriction to positive frequencies and their associated Newton-Wigner states, or the induced Klein-Gordon quantization, that allows both positive and negative frequencies together. We show that the consistent histories approach can give a precise answer to the question concerning the existence of a quantum bounce if and only if one takes the single frequency approach and within a single family of histories, namely, a family containing histories concerning properties of the quantum system at only two specific moments of time: the infinity past and the infinity future. In that case, as shown by Craig and Singh \cite{CS}, there is no quantum bounce. In any other situation, the question concerning the existence of a quantum bounce has no meaning in the consistent histories approach. On the contrary, we show that if one considers the de Broglie-Bohm theory, there are always states where quantum bounces occur in both quantization schemes. Hence the assertion that the Wheeler-DeWitt quantization does not solve the singularity problem in cosmology is not precise. To address this question, one must specify not only the quantum interpretation adopted but also the quantization scheme chosen.Comment: 13 pages, 1 figur

Conductivity of suspended and non-suspended graphene at finite gate voltage

We compute the DC and the optical conductivity of graphene for finite values of the chemical potential by taking into account the effect of disorder, due to mid-gap states (unitary scatterers) and charged impurities, and the effect of both optical and acoustic phonons. The disorder due to mid-gap states is treated in the coherent potential approximation (CPA, a self-consistent approach based on the Dyson equation), whereas that due to charged impurities is also treated via the Dyson equation, with the self-energy computed using second order perturbation theory. The effect of the phonons is also included via the Dyson equation, with the self energy computed using first order perturbation theory. The self-energy due to phonons is computed both using the bare electronic Green's function and the full electronic Green's function, although we show that the effect of disorder on the phonon-propagator is negligible. Our results are in qualitative agreement with recent experiments. Quantitative agreement could be obtained if one assumes water molelcules under the graphene substrate. We also comment on the electron-hole asymmetry observed in the DC conductivity of suspended graphene.Comment: 13 pages, 11 figure