Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach

Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows to define the parameter range (Hubbard U vs spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most Quantum Cluster approaches. Comments on the limits of applicability of the method are also provided.Comment: 7 pages, 7 figures: discussion improved, one figure added, references updated. Matches version published in New J. Phy

On-surface and Subsurface Adsorption of Oxygen on Stepped Ag(210) and Ag(410) Surfaces

The adsorption of atomic oxygen and its inclusion into subsurface sites on Ag(210) and Ag(410) surfaces have been investigated using density functional theory. We find that--in the absence of adatoms on the first metal layer--subsurface adsorption results in strong lattice distortion which makes it energetically unfavoured. However subsurface sites are significantly stabilised when a sufficient amount of O adatoms is present on the surface. At high enough O coverage on the Ag(210) surface the mixed on-surface + subsurface O adsorption is energetically favoured with respect to the on-surface only adsorption. Instead, on the Ag(410) surface, at the coverage we have considered (3/8 ML), the existence of stable terrace sites makes the subsurface O incorporation less favourable. These findings are compatible with the results of recent HREEL experiments which have actually motivated this work.Comment: 8 pages, 4 figures and 1 tabl

Effective average action in statistical physics and quantum field theory

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N)-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.Comment: 34 pages,5 figures,LaTe

Chronic neural probe for simultaneous recording of single-unit, multi-unit, and local field potential activity from multiple brain sites

Drug resistant focal epilepsy can be treated by resecting the epileptic focus requiring a precise focus localization using stereoelectroencephalography (SEEG) probes. As commercial SEEG probes offer only a limited spatial resolution, probes of higher channel count and design freedom enabling the incorporation of macro and microelectrodes would help increasing spatial resolution and thus open new perspectives for investigating mechanisms underlying focal epilepsy and its treatment. This work describes a new fabrication process for SEEG probes with materials and dimensions similar to clinical probes enabling recording single neuron activity at high spatial resolution. Polyimide is used as a biocompatible flexible substrate into which platinum electrodes and leads are... The resulting probe features match those of clinically approved devices. Tests in saline solution confirmed the probe stability and functionality. Probes were implanted into the brain of one monkey (Macaca mulatta), trained to perform different motor tasks. Suitable configurations including up to 128 electrode sites allow the recording of task-related neuronal signals. Probes with 32 and 64 electrode sites were implanted in the posterior parietal cortex. Local field potentials and multi-unit activity were recorded as early as one hour after implantation. Stable single-unit activity was achieved for up to 26 days after implantation of a 64-channel probe. All recorded signals showed modulation during task execution. With the novel probes it is possible to record stable biologically relevant data over a time span exceeding the usual time needed for epileptic focus localization in human patients. This is the first time that single units are recorded along cylindrical polyimide probes chronically implanted 22 mm deep into the brain of a monkey, which suggests the potential usefulness of this probe for human applications

Classical evolution of fractal measures generated by a scalar field on the lattice

We investigate the classical evolution of a $\phi^4$ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a non-integer mass dimension. These configurations resemble the equilibrium state of a critical scalar condensate. The measures of the initial fractal behavior vary in time following the mean field motion. We show that the remnants of the original fractal geometry survive and leave an imprint in the system time averaged observables, even for large times compared to the approximate oscillation period of the mean field, determined by the model parameters. This behavior becomes more transparent in the evolution of a deterministic Cantor-like scalar field configuration. We extend our study to the case of two interacting scalar fields, and we find qualitatively similar results. Therefore, our analysis indicates that the geometrical properties of a critical system initially at equilibrium could sustain for several periods of the field oscillations in the phase of non-equilibrium evolution.Comment: 13 pages, 13 figures, version published at Int. J. Mod. Phys.

Effective Average Action in N=1 Super-Yang-Mills Theory

For N=1 Super-Yang-Mills theory we generalize the effective average action Gamma_k in a manifest supersymmetric way using the superspace formalism. The exact evolution equation for Gamma_k is derived and, introducing as an application a simple truncation, the standard one-loop beta-function of N=1 SYM theory is obtained.Comment: 17 pages, LaTeX, some remarks added, misprints corrected, to appear in Phys. Rev.

Exact Flow Equations and the U(1)-Problem

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.Comment: 22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev.

The beta functions of a scalar theory coupled to gravity

We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational corrections to the beta functions and the anomalous dimension of the scalar field, taking into account threshold effects.Comment: 13 pages, plainTe