Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model

To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight.Comment: 25 pages, 10 figure

Electron-electron interaction and charging effects in graphene quantum dots

We analyze charging effects in graphene quantum dots. Using a simple model, we show that, when the Fermi level is far from the neutrality point, charging effects lead to a shift in the electrostatic potential and the dot shows standard Coulomb blockade features. Near the neutrality point, surface states are partially occupied and the Coulomb interaction leads to a strongly correlated ground state which can be approximated by either a Wigner crystal or a Laughlin like wave function. The existence of strong correlations modify the transport properties which show non equilibrium effects, similar to those predicted for tunneling into other strongly correlated systems.Comment: Extended version accepted for publication at Phys. Rev.

The optical conductivity of graphene in the visible region of the spectrum

We compute the optical conductivity of graphene beyond the usual Dirac cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next nearest neighbor hoping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac cone approximation are surprisingly small (a few percent). Our results help in the interpretation of the experimental results reported by Nair {\it et al.} [Science {\bf 320}, 1308 (2008)].Comment: 8 pages, 6 figure

Phenomenological study of the electronic transport coefficients of graphene

Using a semi-classical approach and input from experiments on the conductivity of graphene, we determine the electronic density dependence of the electronic transport coefficients -- conductivity, thermal conductivity and thermopower -- of doped graphene. Also the electronic density dependence of the optical conductivity is obtained. Finally we show that the classical Hall effect (low field) in graphene has the same form as for the independent electron case, characterized by a parabolic dispersion, as long as the relaxation time is proportional to the momentum.Comment: 4 pages, 1 figur

Effect of Holstein phonons on the electronic properties of graphene

We obtain the self-energy of the electronic propagator due to the presence of Holstein polarons within the first Born approximation. This leads to a renormalization of the Fermi velocity of one percent. We further compute the optical conductivity of the system at the Dirac point and at finite doping within the Kubo-formula. We argue that the effects due to Holstein phonons are negligible and that the Boltzmann approach which does not include inter-band transition and can thus not treat optical phonons due to their high energy of $\hbar\omega_0\sim0.1-0.2$eV, remains valid.Comment: 13 pages, 4 figure

Photonic crystals for nano-light in moir\'e graphene superlattices

Graphene is an atomically thin plasmonic medium that supports highly confined plasmon polaritons, or nano-light, with very low loss. Electronic properties of graphene can be drastically altered when it is laid upon another graphene layer, resulting in a moir\'e superlattice. The relative twist angle between the two layers is a key tuning parameter of the interlayer coupling in thus obtained twisted bilayer graphene (TBG). We studied propagation of plasmon polaritons in TBG by infrared nano-imaging. We discovered that the atomic reconstruction occurring at small twist angles transforms the TBG into a natural plasmon photonic crystal for propagating nano-light. This discovery points to a pathway towards controlling nano-light by exploiting quantum properties of graphene and other atomically layered van der Waals materials eliminating need for arduous top-down nanofabrication

Electron-Phonon Interacation in Quantum Dots: A Solvable Model

The relaxation of electrons in quantum dots via phonon emission is hindered by the discrete nature of the dot levels (phonon bottleneck). In order to clarify the issue theoretically we consider a system of $N$ discrete fermionic states (dot levels) coupled to an unlimited number of bosonic modes with the same energy (dispersionless phonons). In analogy to the Gram-Schmidt orthogonalization procedure, we perform a unitary transformation into new bosonic modes. Since only $N(N+1)/2$ of them couple to the fermions, a numerically exact treatment is possible. The formalism is applied to a GaAs quantum dot with only two electronic levels. If close to resonance with the phonon energy, the electronic transition shows a splitting due to quantum mechanical level repulsion. This is driven mainly by one bosonic mode, whereas the other two provide further polaronic renormalizations. The numerically exact results for the electron spectral function compare favourably with an analytic solution based on degenerate perturbation theory in the basis of shifted oscillator states. In contrast, the widely used selfconsistent first-order Born approximation proves insufficient in describing the rich spectral features.Comment: 8 pages, 4 figure

Changing youth? : continuities and ruptures in transitions into adulthood among Catalan young people

The globalisation process has an impact at the micro-level on life-course patterns: concretely, the trajectories of young people into adulthood are being sharply modified. At a European level, the extension, de-linearisation, reversibility and diversification of youth trajectories have been identified as major changes. However, the extent to which these changes affect young people within each country depends on their respective welfare regimes. This article analyses how the Mediterranean welfare regime shapes youth trajectories among Catalan young people and explores the hypothesis that these constraints will make those trajectories less sensitive to the general trends of change identified at a European level. The research is based on an analysis of the Catalan Youth Survey, an official statistic that contains retrospective data on Educational, Work, Housing and Family transitions. The results offer an integrated typology of youth transitions in Catalonia and show how the persistence of traditional patterns of transition are the logical result of the particular articulation of the welfare regime and cultural patterns among Catalan young people

On the universal AC optical background in graphene

The latest experiments have confirmed the theoretically expected universal value $\pi e^2/2h$ of the ac conductivity of graphene and have revealed departures of the quasiparticle dynamics from predictions for the Dirac fermions in idealized graphene. We present analytical expressions for the ac conductivity in graphene which allow one to study how it is affected by interactions, temperature, external magnetic field and the opening of a gap in the quasiparticle spectrum. We show that the ac conductivity of graphene does not necessarily give a metrologically accurate value of the von Klitzing constant $h/e^2$, because it is depleted by the electron-phonon interaction. In a weak magnetic field the ac conductivity oscillates around the universal value and the Drude peak evolves into a peak at the cyclotron frequency.Comment: 18 pages, 4 figures; v2: to match New J. Phys. (Focus on Graphene issue

Muscle fiber conduction velocity is more affected after eccentric than concentric exercise

It has been shown that mean muscle fiber conduction velocity (CV) can be acutely impaired after eccentric exercise. However, it is not known whether this applies to other exercise modes. Therefore, the purpose of this experiment was to compare the effects of eccentric and concentric exercises on CV, and amplitude and frequency content of surface electromyography (sEMG) signals up to 24 h post-exercise. Multichannel sEMG signals were recorded from biceps brachii muscle of the exercised arm during isometric maximal voluntary contraction (MVC) and electrically evoked contractions induced by motor-point stimulation before, immediately after and 2 h after maximal eccentric (ECC group, N = 12) and concentric (CON group, N = 12) elbow flexor exercises. Isometric MVC decreased in CON by 21.7 ± 12.0% (± SD, p < 0.01) and by 30.0 ± 17.7% (p < 0.001) in ECC immediately post-exercise when compared to baseline. At 2 h post-exercise, ECC showed a reduction in isometric MVC by 24.7 ± 13.7% (p < 0.01) when compared to baseline, while no significant reduction (by 8.0 ± 17.0%, ns) was observed in CON. Similarly, reduction in CV was observed only in ECC both during the isometric MVC (from baseline of 4.16 ± 0.3 to 3.43 ± 0.4 m/s, p < 0.001) and the electrically evoked contractions (from baseline of 4.33 ± 0.4 to 3.82 ± 0.3 m/s, p < 0.001). In conclusion, eccentric exercise can induce a greater and more prolonged reduction in muscle force production capability and CV than concentric exercis